Question

graph the solution to the system of equations:$y = 2x - 5$$2x + y = -1$

Explanation:

Step1: Rewrite second equation to slope-intercept

Rearrange $2x+y=-1$ to $y=-2x-1$.

Step2: Find intercepts for $y=2x-5$

• y-intercept: When $x=0$, $y=2(0)-5=-5$. Point: $(0, -5)$
• x-intercept: When $y=0$, $0=2x-5 \implies x=\frac{5}{2}=2.5$. Point: $(2.5, 0)$

Step3: Find intercepts for $y=-2x-1$

• y-intercept: When $x=0$, $y=-2(0)-1=-1$. Point: $(0, -1)$
• x-intercept: When $y=0$, $0=-2x-1 \implies x=-\frac{1}{2}=-0.5$. Point: $(-0.5, 0)$

Step4: Solve for intersection algebraically

Set $2x-5=-2x-1$
$2x+2x=-1+5$
$4x=4 \implies x=1$
Substitute $x=1$ into $y=2x-5$: $y=2(1)-5=-3$. Intersection: $(1, -3)$

Step5: Match to correct graph

The top graph has lines with intercepts matching $y=2x-5$ (crosses y-axis at -5, x-axis at 2.5) and $y=-2x-1$ (crosses y-axis at -1, x-axis at -0.5), intersecting at $(1, -3)$.

Answer:

The correct graph is the top one (the first grid with lines intersecting at $(1, -3)$).