Question

Solve a System of Equations by Elimination -

$$\begin{gathered} 5x+2y=21 \\ 7x-4y=9 \end{gathered}$$

Short answer

The simplification of Expression will be - $(3,3)$.

Step-by-step solution

Step 1.  Given Information.

Equation - $$\begin{gathered} 5x+2y=21 \\ 7x-4y=9 \end{gathered}$$

Step 2.  To Find

Solve a System of Equations by Elimination and find the value of x and y.

Step 3.  Explanation

Equation -

$$\begin{gathered} 5x+2y=21 \\ 7x-4y=9 \end{gathered}$$

We can eliminate y's by multiplying the first equation by 2-

$$\begin{gathered} (5x+2y)\times 2=21\times 2 \\ 7x-4y=9 \\ 10x+4y=42 \\ 7x-4y=9 \end{gathered}$$

Step 4.  Calculation

The equation become -

$$\begin{gathered} 10x+4y=42 \\ 7x-4y=9 \end{gathered}$$

We Add the x's and y's and constants -

$\begin{array}{l}10x+4y=42\\ \frac{7x-4y=9}{17x=51}\end{array}$

Solve for x -

$x=3$

Substitute $\mathit{x}\mathbf{=}\mathbf{3}$ into the second equation $\mathbf{7}\mathit{x}\mathbf{-}\mathbf{4}\mathit{y}\mathbf{=}\mathbf{9}$, Then Solve for y -

$$\begin{gathered} 7x-4y=9 \\ 7\times 3-4y=9 \\ 21-4y=9 \\ -4y=9-21 \\ -4y=-12 \\ y=3 \end{gathered}$$

Written as $(x,y)$will be $(3,3)$

Step 5.  Check the answer

Check that the ordered pair is a solution to both original equations -

Put $(3,3)$in the equations -

$$\begin{gathered} 5x+2y=21 \\ 5\times 3+2\times 3=21 \\ 15+6=21 \\ 21=21 \\ 7x-4y=9 \\ 7\times 3-4\times 3=9 \\ 21-12=9 \\ 9=9 \end{gathered}$$

The Solution is - $\mathbf{(}\mathbf{3}\mathbf{,}\mathbf{3}\mathbf{)}$