6x+3y=21; 2x+4=22; 2x+6y=-18; 5x+24=-15

Question

Solve the following systems by which ever method.

Answer 1

We can use the graphical method for this one.  First, we need to put each equation in y=mx + b form.  After that, we graph them on the same coordinate system.  We find the point that ALL FOUR equations (lines) have in common. This is known as the point of intersection and is the solution to the system of equations.

 

6x + 3y = 21  ---->  3y = -6x + 21  ----->  y = -2x + 7

 

2x + 4 = 22  ---->  2x = 18  ----> x = 9

 

2x + 6y = -18  ----> 6y = -2x -18  -----> y = -3x - 3

 

5x + 24 = -15  ----->  5x = -39  -----> x = -39/5

 

 

Now we have our equations simplify so that we can graph them.  Lines only intersect when they have different slopes. Since we have 2 lines of the four that are parallel to each with undefined slopes, we will have no solutions.