Question

Find the value of y in the solution to the system of equations shown.

y = 4x - 28
y = 1.5x - 18

Answer 1

`y=-12`

Explanation:

Given system of equations:

`\begin{cases}y = 4x - 28\\y = 1.5x - 18\end{cases}`

Use the method of substitution to solve for x:

`\begin{aligned}y & = y\\\implies 4x-28 & = 1.5x - 18\\4x-1.5x & = -18+28\\2.5x & = 10\\x & = 10 / 2.5\\x & = 4\end{aligned}`

Substitute the found value of x into one of the equations and solve for y:

`\begin{aligned} y & = 4x-28\\\implies y & =4(4)-28\\y & = 16-28\\y & = -12\end{aligned}`

Answer 2

Answer: y = -12

Equation's:

1. y = 4x - 28
2. y = 1.5x - 18

Solve them simultaneously:

4x - 28 = 1.5x - 18

4x - 1.5x = -18 + 28

2.5x = 10

x = 10/2.5 = 4

Now find the value of y:

y = 4x - 28

insert x = 4

y = 4(4) - 28

y = 16 - 28 = -12