Step 1) Solve each equation for 8x8x:
8x - 2y = -48x−2y=−4
8x - 2y + color(red)(2y) = -4 + color(red)(2y)8x−2y+2y=−4+2y
8x - 0 = -4 + 2y8x−0=−4+2y
8x = -4 + 2y8x=−4+2y
2x - 3y = 52x−3y=5
color(red)(4)(2x - 3y) = color(red)(4) xx 54(2x−3y)=4×5
(color(red)(4) xx 2x) - (color(red)(4) xx 3y) = 20(4×2x)−(4×3y)=20
8x - 12y = 208x−12y=20
8x - 12y + color(red)(12y) = 20 + color(red)(12y)8x−12y+12y=20+12y
8x - 0 = 20 + 12y8x−0=20+12y
8x = 20 + 12y8x=20+12y
Step 2) Because the left side of both equations are the same we can equate the right side of both equations and solve for yy:
-4 + 2y = 20 + 12y−4+2y=20+12y
-4 - color(blue)(20) + 2y - color(red)(2y) = 20 - color(blue)(20) + 12y - color(red)(2y)−4−20+2y−2y=20−20+12y−2y
-24 + 0 = 0 + (12 - color(red)(2))y−24+0=0+(12−2)y
-24= 10y−24=10y
-24/color(red)(10)= (10y)/color(red)(10)−2410=10y10
-12/5 = (color(red)(cancel(color(black)(10)))y)/cancel(color(red)(10))
-12/5 = y
y= -12/5
Step 3) Substitute -12/5 for y in either of the equations in Step 1 and calculate x:
8x = -4 + 2y becomes:
8x = -4 + (2 xx -12/5)
8x = -4 + (-24/5)
8x = -4 - 24/5
8x = (5/5 xx -4) - 24/5
8x = -20/5 - 24/5
8x = -44/5
8x xx 1/8 = -44/5 xx 1/8
8/8x = -44/40
x = -11/10
The Solution Is:
x = -11/10 and y= -12/5
Or
(-11/10, -12/5)
