Step 1) Solve the first equation for xx:
0.5x + 4y = -10.5x+4y=−1
0.5x + 4y - color(red)(4y) = -1 - color(red)(4y)0.5x+4y−4y=−1−4y
0.5x + 0 = -1 - 4y0.5x+0=−1−4y
color(red)(2) xx 0.5x = color(red)(2)(-1 - 4y)2×0.5x=2(−1−4y)
1x = (color(red)(2) xx -1) - (color(red)(2) xx 4y)1x=(2×−1)−(2×4y)
x = -2 - 8yx=−2−8y
Step 2) Substitute (-2 - 8y)(−2−8y) for xx in the second equation and solve for yy:
x + 2.5y = 3.5x+2.5y=3.5 becomes:
(-2 - 8y) + 2.5y = 3.5(−2−8y)+2.5y=3.5
-2 - 8y + 2.5y = 3.5−2−8y+2.5y=3.5
color(red)(2) - 2 - 8y + 2.5y = color(red)(2) + 3.52−2−8y+2.5y=2+3.5
0 - 8y + 2.5y = 5.50−8y+2.5y=5.5
-8y + 2.5y = 5.5−8y+2.5y=5.5
(-8 + 2.5)y = 5.5(−8+2.5)y=5.5
-5.5y = 5.5−5.5y=5.5
(-5.5y)/color(red)(-5.5) = 5.5/color(red)(-5.5)−5.5y−5.5=5.5−5.5
(color(red)(cancel(color(black)(-5.5)))y)/cancel(color(red)(-5.5)) = -1
y = -1
Step 3)* Substitute -1 for y in the solution to the first equation at the end of Step 1 and calculate x:
x = -2 - 8y becomes:
x = -2 - (8 * -1)
x = -2 - (-8)
x = -2 + 8
x = 6
The Solution Is: x = 6 and y = -1 or (6, -1)
