Question

Solve the system of equations
-6x+2y=-32
4x+3y=-9

Answer 1

Solve the system of equations
5x-4y=-44
-x+3y=22

Answer 2

To solve the system of equations, we can use the method of substitution or the method of elimination. Let's use the method of substitution.

From the first equation, we can solve for y in terms of x:
-6x + 2y = -32
2y = 6x - 32
y = 3x - 16

Substituting this expression for y in the second equation:
4x + 3(3x - 16) = -9
4x + 9x - 48 = -9
13x - 48 = -9
13x = 39
x = 39 / 13
x = 3

Now substitute the value of x back into the expression for y:
y = 3x - 16
y = 3(3) - 16
y = 9 - 16
y = -7

Therefore, the solution to the system of equations is x = 3 and y = -7.

Answer 3

To solve the system of equations, we can use the method of elimination. Let's begin by multiplying the second equation by 5 to make the coefficients of x match:

-5x + 15y = 110

Now we can add the two equations together to eliminate the x terms:

(5x - 4y) + (-5x + 15y) = (-44) + 110

Simplifying, we get:

11y = 66

Now we can solve for y by dividing both sides of the equation by 11:

y = 66/11
y = 6

Substituting this value of y into the second equation:

-x + 3(6) = 22

Simplifying, we get:

-x + 18 = 22

Now we can solve for x by subtracting 18 from both sides of the equation:

-x = 22 - 18
-x = 4

Multiplying both sides by -1 to isolate x:

x = -4

Therefore, the solution to the system of equations is x = -4 and y = 6.