Question

Without graphing, determine the number of solutions and then classify the system of equations.

$\left\{\begin{array}{l}y=\frac{3}{2}x+1\\ 2x-3y=7\end{array}\right.$

Short answer

The number of solution is one and the system of equations is intersect lines, consistent and independent.

Step-by-step solution

Step 1. Given information.

The system of equations is$\left\{\begin{array}{l}y=\frac{3}{2}x+1\\ 2x-3y=7\end{array}\right.$.

Step 2. Solve the first equation for y and find the slope and y-intercept. 

Find the slope andy-intercept.

$y=\frac{3}{2}x+1$

Hence the slope is$\frac{3}{2}$and the $y$-intercept is 1.

Step 3. Solve the second equation for y and find the slope and y-intercept.

Find the slope and y-intercept.

$$\begin{gathered} 2x-3y=7 \\ 3y=2x-7 \\ y=\frac{2}{3}x-\frac{7}{3} \end{gathered}$$

Here the slope is $\frac{2}{3}$and the y-intercept is $-\frac{7}{3}$.

Step 4. Explain the number of solutions.

• Here the slopes are different.
• The system of equation is intersected lines with one solution and that is consistent and independent.