Question

1. what system of equations has exactly one solution?

a $y=2x-8$
$y=2x+8$
b $y=2x+5$
$5y=10x+25$
c $y=-x+50$
$y=-x-12$
d $y=4x+10$
$y=-4x-3$

Explanation:

Step1: Check slope of system A

Both equations have slope $m=2$ (parallel lines, no intersection)

Step2: Simplify system B

Divide second equation by 5: $y=2x+5$, same as first equation (infinitely many solutions)

Step3: Check slope of system C

Both equations have slope $m=-1$ (parallel lines, no intersection)

Step4: Check slope of system D

First equation slope $m=4$, second slope $m=-4$ (different slopes, one intersection)

Answer:

D. $y=4x+10$; $y=-4x-3$