Lesson 13: Solving Systems by Substitution

Question

Solve this system

Answer 1

Hi Jessica A

(1/5, 6) is where your lines below intersect

Given

You can make a direct substitution for y and solve in terms of x as follows:

5x + 20x + 2 = 7

Combine like terms

25x + 2 = 7

Subtract 2 from both sides of the equation

25x = 5

Divide both sides by 25

x = 1/5

Substitute this value for x in the second equation to solve for y

20x + 2 = y

20(1/5) + 2 = y

4 + 2 = y

6 = y

Check by using this values for x and y in the original equations given

5x + y = 7

5(1/5) + 6 = 7

1 + 6 = 7

7 = 7

And we already know

20x + 2 = y

20(1/5) + 2 = y

4 + 2 = y

6 = y

I hope you find this useful if you have any questions please send me a message.

Answer 2

1.) 5x + y = 7

2.) 20x + 2 = y

Substitute Equation #2 into Equation #1 as follows:

5x + (20x + 2) = 7

5x + 20x + 2 = 7

25x + 2 = 7

25x = 5

x = 5/25 = 1/5 = 0.2

Substitute the x-value into one of the original equations to find the y-value.

20(0.2) + 2 = y → 4 + 2 = y → y = 6

5(0.2) + y = 7 → 1 + y = 7 → y = 6

The solution point to the system of linear equations is (1/5, 6).