Question

Solve this system of equations by graphing. First graph the equations, and then type the solution.y=1/2x–3y=–3/2x+1

Answer 1

Given the system of equations

`\begin{gathered} y\text{ = }(1)/(2)x\text{ - 3 ----- equation 1} \\ y\text{ = -}(3)/(2)x\text{ + 1 -----equation 2} \\ \end{gathered}`

To solve the system of equation by graphing,

Step 1:

Plot the graph of equation 1.

The graph of equation 1 is as shown below:

Step 2:

Plot the graph of equation 2.

The graph of equation 2 is as shown below:

Step 3:

Evaluate the solution.

The solution to the system of equations is evaluated to be the point at which the line graphs intersect.

In the above plot, the graphs intersect at the point (2, -2).

Thus, the solution to the system of equations is

`\begin{gathered} x\text{ = 2} \\ y\text{ = -2} \end{gathered}`