Final answer:
Solve the system using elimination by first obtaining equal coefficients for one variable, then eliminating that variable and solving for the other. In this scenario, x = -3.25 and y = 2.25.
Step-by-step explanation:
To solve the system of equations 6x-2y=-24 and 7x+7y=-7 using the elimination method, you want to eliminate one of the variables by making the coefficients of that variable the same in both equations.
In this case, multiplying the first equation by 7 and the second by 2 gives us:
42x - 14y = -168
14x + 14y = -14
Adding the two equations together eliminates the y term:
56x = -182
Divide both sides by 56 to find the value of x:
x = -182 / 56
= -3.25
Now that you have the value of x, substitute it back into one of the original equations to solve for y. Using the first equation:
6(-3.25) - 2y = -24
-19.5 - 2y = -24
2y = 4.5
y = 4.5 / 2
y = 2.25
After solving, we find that x = -3.25 and y = 2.25.