Q89. - Algebra 1

Question

Use elimination to solve each system of equations.

$$\begin{gathered} \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{2}x+y=\mathbf{5} \\ \mathbf{3}\mathbf{x}\mathbf{-}\mathbf{2}\mathbf{y}\mathbf{=}\mathbf{4} \end{gathered}$$

Step-by-Step Solution

Answer

The solution of the given system of equations is $\left(2,1\right)$.

Step 1. Multiply.

Multiply each side $2x+y=5$ by 2.

$$\begin{gathered} 2\left(2x+y\right)=2\left(5\right) \\ 4x+2y=10 \end{gathered}$$

Step 2. Add.

Add $4x+2y=10$ and $3x-2y=4$. Simplify to obtain the value of x.

$$\begin{gathered} \left(4x+2y\right)+\left(3x-2y\right)=10+4 \\ 7x=14 \\ \frac{7x}{7}=\frac{14}{7} \\ x=2 \end{gathered}$$ 

Step 3. Substitute.

Substitute 2 for x into $2x+y=5$ and simplify.

$$\begin{gathered} 2\left(2\right)+y=5 \\ 4+y-4=5-4 \\ y=1 \end{gathered}$$ 

 

Therefore, the solution of the given system of equations is $\left(2,1\right)$.