Answer:
The solution to the system of equations becomes:
(x, y) = (7, 12)
Step-by-step explanation:
Given the system of equations
[tex]5x - 3y = -1[/tex]
[tex]2x - y = 2[/tex]
Solving using the Elimination Method
[tex]\begin{bmatrix}5x-3y=-1\\ 2x-y=2\end{bmatrix}[/tex]
Multiply 5x - 3y = - 1 by 2: 10x - 6y = -2
Multiply 2x - y = 2 by 5: 10x - 5y = 10
[tex]\begin{bmatrix}10x-6y=-2\\ 10x-5y=10\end{bmatrix}[/tex]
subtraction operation
[tex]10x-5y=10[/tex]
[tex]-[/tex]
[tex]\underline{10x-6y=-2}[/tex]
[tex]y=12[/tex]
so the system of equations becomes
[tex]\begin{bmatrix}10x-6y=-2\\ y=12\end{bmatrix}[/tex]
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)
