4 ways to solve a system of equations

4 ways to solve a system of equations
4 ways to solve a system of equations
Anonim

Solving a system of equations amounts to finding the value of several unknowns using several equations. You can solve a system of equations by addition, subtraction, multiplication, or substitution. If you want to know how to solve a system of equations, just follow these steps.

Steps

Method 1 of 4: Solving by subtraction

Encourages Good Study Habits in a Child Step 2

Step 1. Write the equations one under the other

You can use the subtraction method when both equations have an unknown with the same coefficient and the same sign.

  • For example, if both equations contain 2x, you need to use the subtraction method to find the value of x and y.
  • Write the equations on top of each other, aligning the xs, ys, and constants. Put the subtraction sign to the left of the second equation.
  • Example: if your two equations are 2x + 4y = 8 and 2x + 2y = 2, then you need to align the two equations vertically, with the subtraction sign to the left of the second equation, thus meaning that you are subtracting the two equations from term to term:

    • 2x + 4y = 8
    • - (2x + 2y = 2)
Announce Your Retirement Step 8

Step 2. Subtract term by term

Now that you've got the two equations aligned, all you need to do is subtract similar terms. You can operate term after term as follows:

  • 2x - 2x = 0
  • 4y - 2y = 2y
  • 8 - 2 = 6

    2x + 4y = 8 - (2x + 2y = 2) = 0 + 2y = 6

Apply for an Entrepreneurial Grant Step 14

Step 3. Find the other stranger

Once you've eliminated one of the two unknowns, you just need to find the other unknown (here, y). Take the 0 out of the equation, because it's no use.

  • 2y = 6
  • y = 6/2, or y = 3
Stop Using Racist Comments Step 1

Step 4. Numerically apply one of the equations to find the value of the first unknown

Now that you know that y = 3, you just need to numerically apply one of the equations to find x. No matter which equation you choose, the result will be the same. If one of the equations seems more complicated than the other, choose the simpler.

  • Numerically apply y = 3 of the equation 2x + 2y = 2 to find x.
  • 2x + 2 (3) = 2
  • 2x + 6 = 2
  • 2x = -4
  • x = - 2

    You have solved the system of equations by subtraction. The answer is therefore the couple: (x, y) = (-2, 3)

Defend Against Appropriation of Name or Likeness Claims Step 15

Step 5. Check your answer

To make sure that you have correctly solved your system of equations, do the numerical application with both solutions in both equations to make sure that it works. Here's how to do it.

  • Do the numerical application with (x, y) = (-2, 3) from the equation 2x + 4y = 8.

    • 2(-2) + 4(3) = 8
    • -4 + 12 = 8
    • 8 = 8
  • Do the numerical application with (x, y) = (-2, 3) from the equation 2x + 2y = 2.

    • 2(-2) + 2(3) = 2
    • -4 + 6 = 2
    • 2 = 2

Method 2 of 4: Solving by addition

Study Late at Night Step 5

Step 1. Write the equations one under the other

You can use the addition method when the two equations have an unknown with the same coefficient, but opposite signs. For example, if one of the two equations contains 3x, and the other contains -3x.

  • Write the equations on top of each other, aligning the xs, ys, and constants. Put the addition sign to the left of the second equation.
  • Example: if your two equations are 3x + 6y = 8 and x - 6y = 4, then you need to align the two equations vertically, with the addition sign to the left of the second equation, thus meaning that you add the two equations term in the long term:

    • 3x + 6y = 8
    • + (x - 6y = 4)
Calculate Profit Step 1

Step 2. Add term by term

Now that you've got the two equations aligned, all you need to do is add up the similar terms. You can operate term after term as follows:

  • 3x + x = 4x
  • 6y + -6y = 0
  • 8 + 4 = 12
  • you then get:

    • 3x + 6y = 8
    • + (x - 6y = 4)
    • = 4x ​​+ 0 = 12
Improve Your Life Step 5

Step 3. Find the other stranger

Once you've eliminated one of the two unknowns, you just need to find the other unknown (here, y). Take the 0 out of the equation, because it's no use.

  • 4x + 0 = 12
  • 4x = 12
  • x = 12/4, or x = 3
Write a Grant Proposal Step 5

Step 4. Numerically apply one of the equations to find the value of the first unknown

Now that you know that x = 3, you just need to numerically apply one of the equations to find x. No matter which equation you choose, the result will be the same. If one of the equations seems more complicated than the other, choose the simpler.

  • Numerically apply x = 3 of the equation x - 6y = 4 to find y.
  • 3 - 6y = 4
  • -6y = 1
  • y = 1 / -6, or y = -1/6

    You have solved the system of equations by addition. The answer is therefore the couple: (x, y) = (3, -1/6)

Write a Grant Proposal Step 17

Step 5. Check your answer

To make sure that you have correctly solved your system of equations, do the numerical application with both solutions in both equations to make sure that it works. Here's how to do it.

  • Do the numerical application with (x, y) = (3, 1/6) of the equation 3x + 6y = 8.

    • 3(3) + 6(-1/6) = 8
    • 9 - 1 = 8
    • 8 = 8
  • Do the numerical application with (x, y) = (3, 1/6) of the equation x - 6y = 4.

    • 3 - (6*-1/6) =4
    • 3 - - 1 = 4
    • 3 + 1 = 4
    • 4 = 4

Method 3 of 4: Solving by multiplication

Write a Journal Step 3

Step 1. Write the equations one under the other

Write the equations on top of each other, aligning the xs, ys, and constants. We use the multiplication method when the unknowns have different coefficients … for now!

  • 3x + 2y = 10
  • 2x - y = 2
Overcome Boredom Step 1

Step 2. Multiply one of the two equations, or both, until one of the unknowns has the same coefficient in both equations

Now multiply either or both of the equations by a number so that one of the unknowns has the same coefficient in both equations. In our case, we can multiply the second equation by 2, so that -y becomes -2y, unknown that we have in the first equation with the same coefficient. Which give:

  • 2 (2x - y = 2)
  • 4x - 2y = 4
Write a Grant Proposal Step 12

Step 3. Add or subtract the two equations

Now, it suffices to use either the addition method or the subtraction method in order to eliminate one of the two unknowns. As we have 2y and -2y in our case, we will use the addition method, because 2y + -2y is equal to 0. If you had 2y and 2y, we would have used the subtraction method. Apply here the addition method to eliminate y:

  • 3x + 2y = 10
  • + 4x - 2y = 4
  • 7x + 0 = 14
  • 7x = 14
Accept Mistakes and Learn from Them Step 6

Step 4. Find the other stranger

Solve this simple equation. If 7x = 14, then x = 2.

Deal With Different Problems in Life Step 17

Step 5. Do the numeric application with x = 2 to find the value of the other unknown

Numerically apply one of the equations to find y. No matter which equation you choose, the result will be the same. If one of the equations seems more complicated than the other, choose the simpler.

  • x = 2 - 2x - y = 2
  • 4 - y = 2
  • -y = -2
  • y = 2
  • You have solved the system of equations by multiplication. The answer is therefore the couple: (x, y) = (2, 2)
Define a Problem Step 10

Step 6. Check your answer

To make sure that you have correctly solved your system of equations, do the numerical application with both solutions in both equations to make sure that it works. Here's how to do it.

  • Do the numerical application with (x, y) = (2, 2) of the equation 3x + 2y = 10.
  • 3(2) + 2(2) = 10
  • 6 + 4 = 10
  • 10 = 10
  • Do the numerical application with (x, y) = (2, 2) of the equation 2x - y = 2.
  • 2(2) - 2 = 2
  • 4 - 2 = 2
  • 2 = 2

Method 4 of 4: Solving by substitution

Write a Book Report Step 3

Step 1. Isolate one of the unknowns

The substitution method works well when one of the unknowns has a coefficient of 1 in one of the two equations. Then all you have to do is isolate that unknown.

  • If your two equations are: 2x + 3y = 9 and x + 4y = 2, isolate x in the second equation.
  • x + 4y = 2
  • x = 2 - 4y
Accept Mistakes and Learn from Them Step 4

Step 2. Do the numerical application in the second equation with this unknown factor that you have just isolated

Replace the x value in the second equation with the x value you isolated. Be careful not to do the application with the first equation, which would be pointless! Which give:

  • x = 2 - 4y 2x + 3y = 9
  • 2 (2 - 4y) + 3y = 9
  • 4 - 8y + 3y = 9
  • 4 - 5y = 9
  • -5y = 9 - 4
  • -5y = 5
  • -y = 1
  • y = - 1
Go to College with No Money Step 19

Step 3. Find the other stranger

Since y = - 1, do the numerical map in one of the starting equations to find x. Which give:

  • y = -1 x = 2 - 4y
  • x = 2 - 4 (-1)
  • x = 2 - -4
  • x = 2 + 4
  • x = 6
  • you have solved the system of equations by substitution. The answer is therefore the couple: (x, y) = (6, -1)
End a Letter Step 1

Step 4. Check your answer

To make sure that you have correctly solved your system of equations, do the numerical application with both solutions in both equations to make sure that it works. Here's how to do it.

  • Do the numerical application with (x, y) = (6, -1) from the equation 2x + 3y = 9.

    • 2(6) + 3(-1) = 9
    • 12 - 3 = 9
    • 9 = 9
  • Do the numerical application with (x, y) = (6, -1) of the equation x + 4y = 2.
  • 6 + 4(-1) = 2
  • 6 - 4 = 2
  • 2 = 2

Popular by topic