Question

Solve each system using substitution. Tell whether the system has one solution, infinitely solutions, or no solution.

1.)
2x + y = -12;-4x - 2y = 30

2.)
1/3y = 7/3x + 5/3;x - 3y = 5

3.)
Y = X - 7;3x - 3y = 21

Answer 1

1.
2x + y = -12
-4x - 2y = 30 ---> 2x + y = -15
Clearly two parallel lines. I see the same slope, but different y-intercepts,
So obviously they cannot intersect

2.
1/3y = 7/3x + 5/3 ---> y = 7x + 5
x - 3y = 5

I see different slopes, so they WILL intersect
sub y = 7x + 5 into the 2nd
carry on

3.
Y = X - 7
3x - 3y = 21 ----> x - y = 7 or y = x - 7

They are both the same equation,
any equation will intersect with its self in an infinite number of points.