Question

A system of equations is shown below:

y = 3x − 7
y = 2x + 1

What is the solution to the system of equations?

(8, 17)
(−8, 17)
(−8, −17)
(8, −17)

Answer 1

Here you have two equation and two unknowns, x and y, so this system of equations is solvable. There are a couple of ways of solving these equations.

1) The hardest way is observing that these two equations are lines and you can graph them and where they intersect they are equal for x and y.

2) An easier way is to realize both equations are equal to y, so substitute one of the y's into the other equation and solve for x.

3) The easiest solution is to subtract the lower equation from the upper equation and solve for x.
This technique might be new to you, but just due the subtraction on each related variable. For example:
5x - 2x = 3x,
10y - 15y = -5y
just like regular numbers
15 - 6 = 9 when in the first equation x is 3