# 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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