Question

Solve each system by elimination.-5x + 7y =11-5x + 3y =19Which variable has the same term? Type x or y . Write the solution as an ordered pair (x or y)

Answer 1

Given:

`\begin{gathered} -5x+7y=11 \\ -5x+3y=19 \end{gathered}`

The variable that has the same term is x. This is because the coefficient of x in both equations is -5.

To solve simultaneously by the elimination method, we eliminate the variable that has the same term.

Hence, we eliminate x and solve for y.

To eliminate x, we subtract both equations.

`\begin{gathered} -5x+7y=11\ldots\ldots\ldots\ldots\ldots\ldots\text{.}\mathrm{}(1) \\ -5x+3y=19\ldots\ldots\ldots\ldots\ldots\ldots.(2) \\ \\ \text{Subtracting equation (2) from equation (1),} \\ \text{That is equation (1) - (2);} \\ -5x-(-5x)+7y-3y=11-19 \\ -5x+5x+7y-3y=11-19 \\ 4y=-8 \\ \text{Dividing both sides by 4 to get y,} \\ y=-(8)/(4) \\ y=-2 \end{gathered}`

Substituting the value of y in equation (1) to get x,

`\begin{gathered} -5x+7y=11 \\ -5x+7(-2)=11 \\ -5x-14=11 \\ -5x=11+14 \\ -5x=25 \\ \text{Dividing both sides by -5 to get x,} \\ x=(25)/(-5) \\ x=-5 \end{gathered}`

Therefore, the solution to the system of equations as an ordered pair is,

`(x,y)=(-5,-2)`