Q. 1 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 1–4, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent.

$\left\{\begin{array}{l}-2x+y=-7\\ 4x+3y=9\end{array}\right.$

Step-by-Step Solution

Answer

The solution of the system of equations $\left\{\begin{array}{l}-2x+y=-7\\ 4x+3y=9\end{array}\right.$ is $(3,-1)$

Step 1. Given

The system of equations:

$\left\{\begin{array}{l}-2x+y=-7\\ 4x+3y=9\end{array}\right.$

Step 2. Solve the equation

Multiply the first equation by $2$,

$-4x+2y=-14$

Add the above equation with second equation, we get,

$$\begin{gathered} 5y=-5 \\ y=-1 \end{gathered}$$

Step 3. Find x

Substitute $y=-1$ in the second equation,

$$\begin{gathered} 4x+3y=9 \\ 4x+3(-1)=9 \\ 4x=12 \\ x=3 \end{gathered}$$

Step 4. Check the solution

Substitute $x=3; y=-1$ in the first equation,

$$\begin{gathered} -2x+y=-7 \\ -2\left(3\right)+(-1)=-7 \\ -7=-7 \end{gathered}$$

Hence the solution is checked.