Question

Solve the system of two equations using elimination with multiplication.
4х - 6y = -48
-2x + 4y = 30 (1 point)
A. (-3, 6)
B. (21, -6)
C. (3, 9)
D. (-33, -9)

Answer 1

How many solutions does the system of equations have?
8х - 6y = 48
8x + 6y = 48
A. one
B. infinite
C. none
D. two

Answer 2

To solve the system of equations using elimination with multiplication, we need to eliminate one variable by multiplying one or both of the equations by a constant that will create opposite coefficients for that variable.

In this case, we can see that if we multiply the first equation by 2, and the second equation by 3, the coefficients of x in both equations will become -12 and 6 respectively, which will allow us to eliminate x.

Multiplying the first equation by 2:
8x - 12y = -96

Multiplying the second equation by 3:
-6x + 12y = 90

Now, we can add the two equations together to eliminate y:
(8x - 12y) + (-6x + 12y) = -96 + 90
2x = -6
x = -3

Now that we have the value of x, we can substitute it back into either of the original equations to solve for y. Let's use the first equation:
4(-3) - 6y = -48
-12 - 6y = -48
-6y = -48 + 12
-6y = -36
y = -36/-6
y = 6

Therefore, the solution to the system of equations is (-3, 6), which corresponds to option A. (-3, 6)

Answer 3

To determine the number of solutions the system of equations has, we can simplify the equations and compare them.

If we add the two equations together, we get:
(8x - 6y) + (8x + 6y) = 48 + 48
16x = 96
x = 96/16
x = 6

Now, we substitute the value of x back into one of the original equations, let's use the first one:
8(6) - 6y = 48
48 - 6y = 48
-6y = 48 - 48
-6y = 0
y = 0

We see that the value of y is 0.

Therefore, the system of equations has one solution: (6, 0). The answer is option A. one.