Stuart A. answered • 08/26/26
Undergraduate majors math and chemistry. Masters in chemistry
Looks like you need help on a take home quiz (from 2022). I will assume that the test is long past, and I can answer without exposing you to the temptation to cheat. I am going to go pedantic and go through the steps because that is what tutoring is.
We start out with two equations:
2X - 7Y = -4
8X - 7Y = 26
The whole point is to find an X and a Y value that will make BOTH equations true. The best thing about an equation is that whatever you do to one side of the = sign if you do the same thing to the other side, the equation remains true. So logically if you subtract 8X -7Y from the left side of the top equation and 26 from the right side it remains true. So, if we do that subtraction we get:
-6X + 0Y = -30
the 0Y term is just 0 times Y do we can drop it
-6X = -30 You are now down to a single equation with a single unknown. So, the rest is just arithmetic.
divide both sides by -6:
X = 5
If you substitute 6 for the X in the top equation you get:
2(5) - 7Y = -4
10 - 7Y = -4 Once again single equation, single unknown. But not simple arithmetic just yet
subtract 10 from each side:
-7Y = -14 Now we are back to arithmetic.
divide each side by -7:
Y = 2
so as an ordered pair: X = 5. Y = 2 or (5,2)
