Question

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

Answer 1

(x, y) = ( $\frac{31}{8}$, $\frac{25}{8}$)

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 = $\frac{31}{8}$

Substitute this value into (3) for y

y = 7 - x = $\frac{56}{8}$ - $\frac{31}{8}$ = $\frac{25}{8}$