Final answer:
To combine the equations, you multiply the first equation by 3 to equalize the y coefficients. Combining these equations, they do not simplify to a valid equation.
Step-by-step explanation:
To combine the equations (2x - y = 16) and (-6x + 3y = -36), you want to manipulate them so that adding or subtracting one equation from the other will eliminate one of the variables. In this case, you can multiply the first equation by 3 to make the coefficients of y in both equations equal, but opposite in sign.
First equation after multiplying by 3: (2x - y) * 3 = 16 * 3, which gives us 6x - 3y = 48.
Add this to the second equation: (6x - 3y) + (-6x + 3y) = 48 - 36, which gives us 0x + 0y = 12. This appears to be a mistake because the result is not possible (0 = 12 is not a valid equation). Let's review the second equation: it might be a typo since the term 6x cancels itself, suggesting the correct form should probably be -6x + 3y = -36. Adding the modified equations together, we cancel y and find the value for x:
Simplified combined equation: (6x + (-6x)) + (-3y + 3y) = 48 + (-36), giving us 0x + 0y = 12
If the second equation is in fact correct as given (-6x + 6x = -36), it appears to have an error as -6x + 6x should equal 0. If we continue with the assumption that it is -6x + 3y = -36, then after combining the equations correctly, we would solve for x:
6x - 6x - 3y + 3y = 48 - 36
0 - 0y = 12, which is not possible.