Answer:
Step-by-step explanation:
Given system of equations
[tex]\textsf{Equation 1}:\quad x-y=-2[/tex]
[tex]\textsf{Equation 2}:\quad x-y=2[/tex]
Rewrite each equation to make y the subject.
Input x = 0 into the equation to find the y-intercept.
Input y = 0 into the equation to find the x-intercept.
Input x = 4 into the equation to find a third ordered pair.
Plots the points on the graph and draw a line through them.
Equation 1
[tex]\begin{aligned}x-y &=-2\\ \implies -y&=-x-2\\y&=x+2\end{aligned}[/tex]
[tex]x=0 \implies y=0+2=2 \implies (0,2)[/tex]
[tex]y=0 \implies x+2=0 \implies x=-2 \implies (-2,0)[/tex]
[tex]x=4 \implies y=4+2=6 \implies (4,6)[/tex]
Equation 2
[tex]\begin{aligned}x-y& =2\\\implies -y &=-x+2\\y & = x-2\end{aligned}[/tex]
[tex]x=0 \implies y=0-2=-2 \implies (0,-2)[/tex]
[tex]y=0 \implies x-2=0 \implies x=2 \implies (2,0)[/tex]
[tex]x=4 \implies y=4-2=2 \implies (4,2)[/tex]
Slope-intercept form of a linear equation: [tex]y=mx+b[/tex]
(where m is the slope and b is the y-intercept)
Comparing both equations:
- Same slopes
- Different y-intercepts
Therefore, the lines are parallel. This is called Inconsistent and means the system of equations has no solution (since the lines never intersect).
