Q19. - Algebra 1

Question

Use elimination to solve each system of equations.  

 

$$\begin{gathered} -5x+2y=-11 \\ 5x-7y=1 \end{gathered}$$

Step-by-Step Solution

Answer

The required solution is represented by $x=3$ and $y=2$.

Step 1. Number the provided equations.

Make consideration that,

 

$$\begin{gathered} -5x+2y=-11\mathrm{......}\left(1\right) \\ 5x-7y=1\mathrm{......}\left(2\right) \end{gathered}$$

Step 2. Perform addition between the provided equations to get the value of y after it use the obtained value to get the value of x .

Perform addition between the equation (1) and equation (2) to extract the value of y. 

 

$$\begin{gathered} \left(-5x+2y\right)+\left(5x-7y\right)=-11+1 \\ -5x+2y+5x-7y=-10 \\ 2y-7y=-10 \\ -5y=-10 \\ y=\frac{-10}{-5} \\ y=2 \end{gathered}$$

 

Use the obtained value of y into equation (1) to get the value of x.

 

$$\begin{gathered} -5x+2\times 2=-11 \\ -5x+4=-11 \\ -5x=-11-4 \\ -5x=-15 \\ x=\frac{-15}{-5} \\ x=3 \end{gathered}$$

Step 3. Write the conclusion.

The obtained value of x and y represents the required solution that is $x=3$ and $y=2$.