Question

Solve the linear system by graphing.

$\begin{array}{l}y=-3x+7\\ y=3x+4\end{array}$

Short answer

Solution of the given system is$\left(\frac{1}{2},\frac{11}{2}\right)$.

Step-by-step solution

Step 1. Given Information.

Linear system is:

$\begin{array}{l}y=-3x+7\\ y=3x+4\end{array}$,

Step 2. Property used.

Substitution property.

Step 3. Calculation.

For equation: $y=-3x+7$

Put the value of x in y, Hence,

For equation: $y=3x+4$

Put the value of x in y, Hence,

Now, both lines meet at pointlocalid="1649433865504" $\left(\frac{1}{2},\frac{11}{2}\right)$.

Equation 1: $y=-3x+7$

Equation 2: $y=3x+4$

By substituting the value of y from equation 1 to equation 2.

$\begin{array}{c}-3x+7=3x+4\\ 6x=3\\ x=\frac{3}{6}\\ =\frac{1}{2}\end{array}$

Now substituting the value of x in equation 1.

$\begin{array}{c}y=-3\left(\frac{1}{2}\right)+7\\ =-\frac{3}{2}+7\\ =\frac{11}{2}\end{array}$

Hence, both lines meet at point$\left(\frac{1}{2},\frac{11}{2}\right)$.

Step 4. Conclusion.

The solution to the given linear system is$\left(\frac{1}{2},\frac{11}{2}\right)$.