Final answer:
To solve the given system of linear equations by combining, we first multiplied the second equation by 3.5 to align the coefficients of x. We then added the two equations to eliminate x, finding y = -9.25. Finally, we substituted y into one of the original equations to solve for x, yielding x = 5.25.
Step-by-step explanation:
To solve the system of equations -7x+y=-46 and -2x+2y=-8 by combining the equations, we first look for a way to eliminate one of the variables by adding or subtracting the equations from each other. Let's multiply the second equation by 3.5 (to get the coefficient of x to be 7, the same as the coefficient in the first equation but with the opposite sign).
Multiplying the second equation by 3.5 gives -7x+7y=-28.
Now we can add this equation to the first equation:
- -7x + y = -46
- -7x + 7y = -28
Adding these two equations, the x terms cancel out, and we are left with 8y = -74. Dividing both sides by 8 gives us y = -9.25.
Now we substitute y = -9.25 into one of the original equations, for example, the first equation -7x + y = -46, to find x:
- -7x + (-9.25) = -46
- -7x = -46 + 9.25
- -7x = -36.75
- x = 5.25
Hence, the solution to the system of equations is x = 5.25 and y = -9.25.