Final answer:
To solve the system of equations by elimination, multiply the equations to eliminate one variable, solve for the remaining variable, and verify the solution by substituting it back into the original equations.
Step-by-step explanation:
To solve the system of equations by elimination, we want to eliminate one variable by adding or subtracting the equations together. In this case, we can eliminate the variable x by multiplying the first equation by 2 and the second equation by 7. This gives us:
14x + 6y = -24
14x + 35y = 266
Subtracting the first equation from the second equation, we get:
0x + 29y = 290
Dividing both sides of the equation by 29, we find that y = 10.
Plugging this value of y back into one of the original equations, we can solve for x:
7x + 3(10) = -12
7x + 30 = -12
7x = -42
x = -6
Therefore, the solution to the system of equations is x = -6 and y = 10.
To verify our solution, we substitute the values of x and y back into the original equations:
7(-6) + 3(10) = -42 + 30 = -12
2(-6) + 5(10) = -12 + 50 = 38
The values on both sides of the equations match, so our solution is correct.