Chapter 3, Problem 3MCQ

To determine

To calculate: The solution set for the system of equations with the help of a graph.

  $\begin{array}{c}x=2y-4\\ x=-3y+1\end{array}$

Answer to Problem 3MCQ

The solution set for the system of equations is $\left(-2,1\right)$ .

Explanation of Solution

Given information:

The system of equations

  $\begin{array}{c}x=2y-4\\ x=-3y+1\end{array}$

Formula used:

The slope intercept of a line is $y=mx+c$ where m is the slope and c is the intercept of y -axis.

Calculation:

Consider the system of equations

  $\begin{array}{c}x=2y-4\\ x=-3y+1\end{array}$

Write both the equation in slope intercept form.

  $\begin{array}{c}x=2y-4\\ 2y=x+4\\ y=\frac{1}{2}x+2\end{array}$

And,

  $\begin{array}{c}x=-3y+1\\ 3y=1-x\\ y=-\frac{1}{3}x+\frac{1}{2}\end{array}$

Plot the equations $y=\frac{1}{2}x+2$ and $y=-\frac{1}{3}x+\frac{1}{2}$ on the coordinate plane.

  

Red line depicts the equation $x=2y-4$ and blue line depicts the equation $x=-3y+1$ .

The graph of the equations intersect at $\left(-2,1\right)$ .

Therefore, the solution set of the system of equations is $\left(-2,1\right)$ .

To verify substitute the point $\left(-2,1\right)$ in the equations and check.

For the equation $x=2y-4$ , substitute x as $-2$ and y as $1$ .

  $\begin{array}{c}-2=2\left(-1\right)-4\\ -2=-2\end{array}$

For the equation $x=-3y+1$ , substitute x as $-2$ and y as $1$ .

  $\begin{array}{c}-2=-3\left(1\right)+1\\ -2=-2\end{array}$

Both the equations satisfy the point.

Thus, the solution set for the system of equations is $\left(-2,1\right)$ .