Online Algebra Tutoring: Simultaneous Equations (Substitution)

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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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