Question

5x + 2y = 24
5y = x + 6
What is the solution to the system?

Answer 1

Answer: (4, 2) or x = 4, y = 2

Solving by substitution:

Given:

5x + 2y = 24

5y = x + 6

Setting one equation equal to y:

2y = -5x + 24

y =
`(-5)/(2)`x + 12

Substituting:

5y = x + 6

5(
`(-5)/(2)`x + 12) = x + 6

`(-25)/(2)`x + 60 = x + 6

`(-25)/(2)`x + 54 = x

54 =
`(27x)/(2)`

108 = 27x

4 = x

Plug x = 4 into an equation to solve for y:

5y = x + 6

5y = (4) + 6

5y = 10

y = 2

Solving by graphing:

The solution is the point of intersection.

-> See attached