Online Algebra Tutoring: Simultaneous Equations (Substitution)

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Learn Simultaneous Equations  from  Online Algebra Tutor

In this method, we choose any one equation from the given set of two equations and we solve that equation for y, we substitute the value of y into the other equation. After putting the value of y in the other equation, we get equation in only one variable that is x, we can solve this equation and substitute the value of x into any one equation.

Example: a) y + x = 8 equation 1
b) y – 2x = 11 equation 2

Step 1: Choose the first equation and solve for y.
y = 8 – x

Step 2: We plug in this value of y into equation 2.
y – 2x = 11
8 – x – 2x = 11
8 – 3x = 11

Step 3: Subtract 8 from both sides.
8 – 8 – 3x = 11 – 8
-3x = 3

Divide both sides by -3.
(-3x / -3) = 3 / -3
x = -1

Step 4: Plug in x = -1 back into the first equation.
y + x = 8
y – 1 = 8

Solution: y=9 and x = -1.

Checkpoint:

Solve system of linear equations by substitution method:

1.)y = x – 1 , 2x − 3y = −1
2.)x – 9y = –24, x + 7y = 24
3.)x + y = –5, 3x + y = –21
4.)−3x + 3y = 3, −5x + y = 13
5.)−7x + 8y = −5, −2x + 6y = 6

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