Q 31 - Intermediate Algebra

Question

Solve the systems of equations by substitution. 

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

Step-by-Step Solution

Answer

The solution of system of linear equation is $(1,-4)$

Step 1. Given information

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

Step 2. Substitute the value of y from one equation into other equation

$$\begin{gathered} 2x+y=-2 \\ y=-2x-2 \end{gathered}$$

Now,

$$\begin{gathered} 3x-y=7 \\ 3x-(-2x-2)=7 \\ 3x+2x+2=7 \\ 5x=5 \\ x=1 \end{gathered}$$

Step 3. Substitute the value of x in any equation

$$\begin{gathered} 2x+y=-2 \\ 2\left(1\right)+y=-2 \\ y=-4 \end{gathered}$$

Step 4. Required answer

The solution of system of linear equation is $(1,-4)$