Question

lukas graphed the system of equations shown.
$2x + 3y = 2$
$y = \frac{1}{2}x + 3$

Explanation:

Assuming the problem is to find the solution (intersection point) of the system of equations.

Step1: Recall the solution of a system of equations from a graph

The solution of a system of linear equations graphed is the point where the two lines intersect.

Step2: Identify the intersection point from the graph

Looking at the graph, the two lines (red for \(2x + 3y=2\) and blue for \(y = \frac{1}{2}x+3\)) intersect at the point \((-2, 2)\). We can also verify this by substituting \(x=-2\) and \(y = 2\) into both equations.

For the first equation \(2x+3y\):
Substitute \(x=-2\), \(y = 2\): \(2(-2)+3(2)=- 4 + 6=2\), which matches the right - hand side of \(2x + 3y = 2\).

For the second equation \(y=\frac{1}{2}x + 3\):
Substitute \(x=-2\): \(y=\frac{1}{2}(-2)+3=-1 + 3=2\), which matches the \(y\) - value of the point.

Answer:

The solution of the system of equations is \((-2,2)\)