Question

Solve the system of equations by graphing. y=1/3x+33x-y=5

Answer 1

Answer:

The solution to the system of equations is the point at which the two lines meet:

$\begin{gathered} (3,4) \\ x=3 \\ y=4 \end{gathered}$

Explanation:

Given the system of equation;

$\begin{gathered} y=\frac{1}{3}x+3\text{ ---1} \\ 3x-y=5\text{ ---2} \end{gathered}$

rewrite equation 2 in slope intercept form;

$\begin{gathered} 3x-y=5 \\ y=3x-5\text{ ----2a} \end{gathered}$

Let us derive two cordinate points for each equation;

$\begin{gathered} y=\frac{1}{3}x+3\text{ ---1} \\ at\text{ x=0;} \\ y=\frac{1}{3}(0)+3 \\ y=3 \\ (0,3) \\ at\text{ x=3;} \\ y=\frac{1}{3}(3)+3 \\ y=1+3 \\ y=4 \\ (3,4) \end{gathered}$$\begin{gathered} y=3x-5\text{ ----2a} \\ at\text{ x=0;} \\ y=3(0)-5 \\ y=-5 \\ (0,-5) \\ \text{at x=3;} \\ y=3(3)-5 \\ y=9-5 \\ y=4 \\ (3,4) \end{gathered}$

Plotting the coordinate points on the graph we have;

Graphing the two equations, the solution to the system of equations is the point at which the two lines meet.

$\begin{gathered} (3,4) \\ x=3 \\ y=4 \end{gathered}$