Question

Solve the system of equations.
−6x+2y=−32
4x+3y=−9 (1 point)
( , )

Answer 1

To solve the system of equations:

1) Set up both equations:
-6x + 2y = -32
4x + 3y = -9

2) Multiply the first equation by 2 to eliminate x:
-12x + 4y = -64

3) Add the second equation to this new equation:
-12x + 4y + 4x + 3y = -64 + (-9)
-8x + 7y = -73

4) Divide the new equation by -1 to simplify:
8x - 7y = 73

5) Now you can solve the system of equations by adding the new equation to the second equation:
8x - 7y + 4x + 3y = 73 + (-9)
12x - 4y = 64

6) Multiply the second equation by 2 to eliminate y:
24x - 8y = 128

7) Add the first equation to this new equation:
24x - 8y + 12x - 4y = 128 + (-64)
36x - 12y = 64

8) Divide the new equation by 4 to simplify:
9x - 3y = 16

9) You can see that the new equation is equivalent to the third equation: 9x - 3y = 16

10) Since the two new equations are the same, they represent the same line. Thus, there are infinitely many solutions to the system of equations.

Therefore, the system of equations (−6x + 2y = −32, 4x + 3y = −9) has infinitely many solutions and cannot be expressed as a single coordinate point.