what is the answer

Question

x=2y-4

2x+y=2

Answer 1

Hello! This is a systems of equations problem. There are 3 methods to solve systems of equations: graphing, substitution, and elimination. Since one variable (x) is already alone on one side of the equation for the top equation, substitution would be the easiest method.

x = 2y - 4

2x + y = 2

First, we take what x equals in the top equation (2y - 4) and substitute or replace x with it. We need to use parenthesis because x has a coefficient of 2.

2(2y-4) + y = 2 Now, we distribute the 2.

4y - 8 + y = 2 Next, combine like-terms (4y and y).

5y - 8 = 2

Then get rid of the constant (I like to call this the loose number because it doesn’t have a variable attached to it), which is -8. We do the opposite, so we add 8 to both sides.

5y = 10 Let’s divide by 5 on both sides to get y alone.

y = 2 Once we get the value for one variable, plug it back into one of the original equations to solve for the other variable (in this case, we solve for x).

original equation: x = 2y - 4

plug in 2 for y: x = 2(2) - 4

x = 4 - 4

x = 0

Usually, we write our answer as an ordered pair (x, y).

Answer: (0, 2)

I hope that helped you!