Question

Solve the following system of equations by the substitution method.

5x = y + 6
2x - 3y = 4

What is the value of the y-coordinate?
-8/13
13/14
14/13

Answer 1

Answer: y = -8/13

The value of the y coordinate is

-8/13

Answer 2

5x = y + 6 (I)
2x - 3y = 4 (II)
-------------------
We have:
5x = y + 6 →
`x = (y+6)/(5)`

Soon:
2x - 3y = 4 →
`2* ((y+6)/(5)) - 3y = 4\to (2y+12)/(5) - 3y = 4`
least common multiple (5)

`(2y+12)/(5) - 3y = 4\to (2y+12)/(\diagup\!\!\!\!\!5) - (15y)/(\diagup\!\!\!\!\!5) = (20)/(\diagup\!\!\!\!\!5)`

`2y + 12 - 15y = 20`

`- 15y + 2y = 20 - 12`

`- 13y = 8`

`\boxed{\boxed{y = - (8)/(13) }}\end{array}}\qquad\quad\checkmark`