Question

What is the solution set for the following system of equations 5x-3y-10=0 x+y-7=0

Answer 1

(x, y) = (
`(31)/(8)`,
`(25)/(8)`)

given the 2 equations

5x - 3y - 10 = 0 → (1)

x + y - 7 = 0 → (2)

rearrange (2) to obtain y in terms of x

y = 7 - x → (3)

Substitute y = 7 - x into (1)

5x - 3(7 - x) - 10 = 0

5x - 21 + 3x - 10 = 0

8x - 31 = 0 ( add 31 to both sides )

8x = 31 ( divide both sides by 8 )

x =
`(31)/(8)`

Substitute this value into (3) for y

y = 7 - x =
`(56)/(8)` -
`(31)/(8)` =
`(25)/(8)`