The solution to the system of equations below is (x,y). 3x+y=13 2x-4y=18

Question

The solution to the system of equations below is (x,y). 3x+y=13 2x-4y=18

3x+y=13

2x-4y=18

what is the value of x? (____,y)

Answer 1

There are several ways of solving these types of problems. One way is substitution. To use substitution, solve one of the equations for either "x" or "y" and then plug the result into the other equation. In this case, we could solve the first equation (3x+y=13) for y by subtracting 3x from both sides. That would result in y = -3x + 13. Now we can substitute "-3x + 13" into the other equation wherever there is a "y" like this:

2x - 4y = 18

2x - 4(-3x + 13) = 18 [now solve distributing and then by combining like terms like this:

2x + 12x - 52 = 18

14x = 70

x = 5

Although the problem is only looking for that value of "x", you could now also solve for "y", using the equation y = -3x + 13, by plugging in x = 5 like this:

y = -3x + 13

y = -3(5) + 13

y = -15 + 13

y = -2