Question

Solve a System of Equations by Elimination -

$$\begin{gathered} 2x-5y=7 \\ 3x-y=17 \end{gathered}$$

Short answer

The simplification of Expression will be - $(6,1)$.

Step-by-step solution

Step 1.  Given Information.

Equation -$$\begin{gathered} 2x-5y=7 \\ 3x-y=17 \end{gathered}$$

Step 2.  To Find

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

Step 3.  Explanation

Equation -

$$\begin{gathered} 2x-5y=7 \\ 3x-y=17 \end{gathered}$$

We can eliminate y's by multiplying the second equation by 5 -

$$\begin{gathered} 2x-5y=7 \\ (3x-y)\times 5=17\times 5 \\ 2x-5y=7 \\ 15x-5y=85 \end{gathered}$$

Step 4.  Calculation

The equation become -

$$\begin{gathered} 2x-5y=7 \\ 15x-5y=85 \end{gathered}$$

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

$\begin{array}{l}2x-5y=7\\ \frac{15x-5y=85}{-13x=-78}\end{array}$

Solve for x -

$x=6$

Substitute $\mathit{x}\mathbf{=}\mathbf{6}$into the second equation $\mathbf{3}\mathit{x}\mathbf{-}\mathit{y}\mathbf{=}\mathbf{17}$, Then Solve for y -

$$\begin{gathered} 3x-y=17 \\ 3\times 6-y=17 \\ 18-y=17 \\ -y=-1 \\ y=1 \end{gathered}$$

Written as $(x,y)$will be $(6,1)$

Step 5.  Check the answer

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

Put $(6,1)$in the equations -

$$\begin{gathered} 2x-5y=7 \\ 2\times 6-5\times 1=7 \\ 12-5=7 \\ 7=7 \end{gathered}$$

$$\begin{gathered} 3x-y=17 \\ 3\times 6-1=17 \\ 18-1=17 \\ 17=17 \end{gathered}$$

The Solution is - $\mathbf{(}\mathbf{6}\mathbf{,}\mathbf{1}\mathbf{)}$