Question

which graph shows the solution to the system of linear equations?
y = 3x - 3
y = x + 1

Explanation:

Step1: Set equations equal to each other

Since $y = 3x - 3$ and $y = x + 1$, set $3x - 3 = x + 1$.

Step2: Solve for $x$

Subtract $x$ from both sides: $2x - 3 = 1$. Add 3 to both sides: $2x = 4$. Divide by 2: $x = 2$.

Step3: Find $y$ value

Substitute $x=2$ into $y = x + 1$: $y = 2 + 1 = 3$.

Step4: Identify key line features

For $y=3x-3$: slope $m=3$, y-intercept $(0,-3)$. For $y=x+1$: slope $m=1$, y-intercept $(0,1)$. The solution is their intersection point.

Answer:

The graph that shows two lines intersecting at the point $(2, 3)$, with one line having a slope of 3 and y-intercept at $(0, -3)$, and the other line having a slope of 1 and y-intercept at $(0, 1)$. The exact solution point is $\boldsymbol{(2, 3)}$.