Solve each system of equations by graphing.

4.$\begin{array}{c}y=2x+9\\ y=-x+3\end{array}$

Equation of line in slope intercept form is expressed below.

$y=mx+c$

Where m is the slope and c is the intercept of y-axis.

Consider the first equation $y=2x+9$.

The equation is in the form $y=mx+c$. Here slope m of the line is 2 and intercept of y-axis c is 9.

Now, consider the second equation $y=-x+3$. The equation is in the form $y=mx+c$. Here slope m of the line is $-1$ and intercept of y-axis c is 3.

Plot the equations on the same plane and the point where both the equations intersect is the solution of the system of the equations.

The red line denotes the equation $y=2x+9$ and blue line denotes the equation $y=-x+3$.

Therefore, the point of intersection is $\left(-2,5\right)$.

The point of intersection is solution of system of equations if the point satisfies both the equation.

Substitute the point $\left(-2,5\right)$in the equation $y=2x+9$.

Substitute x as 1 and y as $-2$and check whether right hand side is equal to left hand side of the equation.

$\begin{array}{c}5=2\left(-2\right)+9\\ 5=-4+9\\ 5=5\end{array}$

Since, this is true so the point $\left(-2,5\right)$satisfy the equation $y=2x+9$.

Substitute the point $\left(-2,5\right)$in the equation $y=-x+3$.

Substitute x as 1 and y as $-2$and check whether right hand side is equal to left hand side of the equation.

$\begin{array}{l}5=-\left(-2\right)+3\\ 5=2+3\\ 5=5\end{array}$

Since, this is true so the point $\left(-2,5\right)$ satisfy the equation $y=-x+3$.

Hence, the solution of the system of equations is $\left(-2,5\right)$.