(x, y) = ( [tex]\frac{31}{8}[/tex], [tex]\frac{25}{8}[/tex])
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 = [tex]\frac{31}{8}[/tex]
Substitute this value into (3) for y
y = 7 - x = [tex]\frac{56}{8}[/tex] - [tex]\frac{31}{8}[/tex] = [tex]\frac{25}{8}[/tex]
