x + 5y = -15
y = (1/5) x + 1 sub the second into the first for y and we have
x + 5 ( 1/5 x + 1) = -15
x + x + 5 = -15
2x + 5 = -15 subtract 5 from both sides
2x = -20 divide both sides by 2
x = -10
And using y = (1/5)x + 1 to find x, we have y =(1/5) (-10) + 1 = -2 + 1 = -1
So (x , y) = ( -10 , -1)
x + y = 6
x = y + 4 sub the second into the first for x
(y + 4) + y = 6
2y + 4 = 6
2y = 2
y = 1
And x = y + 4 = 1 + 4 = 5
So (x, y) = ( 5 , 1)
2x - 3y = -27 multiply through by 3 ⇒ 6x - 9y = -81 (1)
-3x + 2y = 23 multiply through by 2 ⇒ -6x + 4y = 46 (2)
Add (1) and (2) and we get
-5y = -35 divide both sides by -5
y = 7
And using 2x - 3y = -27 to find x we get
2x - 3(7) = -27
2x - 21 = -27 add 21 to both sides
2x = -6 divide both sids by 2
x = -3
So (x ,y ) = ( -3, 7)