Question

Solve the system of linear equations using ELIMINATION. Write your final solution as an ORDERED PAIR.

5x-3y=x1
2x-y=2

Answer 1

The solution to the system of equations becomes:

(x, y) = (7, 12)

Explanation:

Given the system of equations

`5x - 3y = -1`

`2x - y = 2`

Solving using the Elimination Method

`\begin{bmatrix}5x-3y=-1\\ 2x-y=2\end{bmatrix}`

Multiply 5x - 3y = - 1 by 2: 10x - 6y = -2

Multiply 2x - y = 2 by 5: 10x - 5y = 10

`\begin{bmatrix}10x-6y=-2\\ 10x-5y=10\end{bmatrix}`

subtraction operation

`10x-5y=10`

`-`

`\underline{10x-6y=-2}`

`y=12`

so the system of equations becomes

`\begin{bmatrix}10x-6y=-2\\ y=12\end{bmatrix}`

Therefore, the value of y = 12

For 10x - 6y = -2 plug in y = 12

10x - 6y = -2

10x - 6(12) = -2

10x - 72 = -2

10x = -2+72

10x = 70

dividing both sides by 10

10x/10 = 70/10

x = 7

Therefore, the value of x = 7

Thus, the solution to the system of equations becomes:

(x, y) = (7, 12)