91Ó°ÊÓ

The system of equations are

$$\begin{gathered} -x+y=1 \\ 3x+2y=12 \end{gathered}$$

First equation:

$-x+y=1$

Finding x-intercept

$$\begin{gathered} -x+0=1 \\ -x=1 \\ x=-1 \end{gathered}$$

So, x-intercept is $(-1,0)$

Finding y-intercept

$$\begin{gathered} -0+y=1 \\ y=1 \end{gathered}$$

So, y-intercept is$(0,1)$

Second equation:

$3x+2y=12$

Finding x-intercept

$$\begin{gathered} 3x+2×0=12 \\ 3x+0=12 \\ 3x=12 \\ \frac{3x}{3}=\frac{12}{3} \\ x=4 \end{gathered}$$

So, x-intercept is $(4,0)$

Finding y-intercept

$$\begin{gathered} 3×0+2y=12 \\ 0+2y=12 \\ 2y=12 \\ \frac{2y}{2}=\frac{12}{2} \\ y=6 \end{gathered}$$

So, y-intercept is$(0,6)$

Find equation:

Locate points$(-1,0),(0,1)$ on the graph and then join them to get the line

Second equation:

Locate points$(4,0),(0,6)$ on the graph and then join them to get the line

So, the graph is

If the lines intersect, identify the point of intersection.

If lines are parallel, the system has no solution.

If lines are the same, the system has an infinite number of solutions.

The graph is

Here, the intersection point is $(2,3)$

So, the solution is$(2,3)$.