Calculus row operations

Question

Solve the system using matrices (row operations)

{ -2x -y = 1,

{ 3x -y = -4.

How many solutions are there to this system?

If there is one solution, give its coordinates in the answer spaces below.

If there are infinitely many solutions, enter t in the answer blank for y and enter a formula for x in terms of t in the answer blank for x.

If there are no solutions, leave the answer blanks for x and y empty.

X =

Y =

Answer 1

Actually the answer is x=-1, y=1.

graph y=-2x-1 and y=3x+4 to verify intersection point at (-1,1)

-2x-y=1

3x-y=-4

multiply first equation by -1 and add that equation to second equation

5x=-5,,,,x=-1

Answer 2

x=-1

y=1

just one solution

(x,y) = (-1,1)

if the problem had

been

-3x-y =-4

-2x-y =1

the solution would be

x=5

y=-11