Question

Solve the system of two equations using elimination with multiplication.
4x−6y=−48
−2x+4y=30 (1 point)

Answer 1

no

Answer 2

no it does not

Answer 3

We can start by multiplying the first equation by 2 and the second equation by 3 to eliminate the variable "x":

(2)(4x-6y) = (2)(-48)
-4x + 8y = 60

(3)(-2x+4y) = (3)(30)
-6x + 12y = 90

Now we have the equations:
-4x + 8y = 60
-6x + 12y = 90

We can now add these two equations together to eliminate the variable "x":

(-4x + 8y) + (-6x + 12y) = 60 + 90
-10x + 20y = 150

Now we can divide this equation by -10:
-10x/(-10) + 20y/(-10) = 150/(-10)
x - 2y = -15

Now we have the equations:
x - 2y = -15 (equation 1)
-2x + 4y = 30 (equation 2)

We can multiply equation 1 by 2 to eliminate the variable "x":

2(x - 2y) = 2(-15)
2x - 4y = -30

Now we have the equations:
2x - 4y = -30 (equation 3)
-2x + 4y = 30 (equation 2)

We can add equation 3 and equation 2 together to eliminate the variable "x":

(2x - 4y) + (-2x + 4y) = -30 + 30
0 = 0

Since 0=0, this means the two equations are dependent and graphically represents the same line. Therefore, there are infinitely many solutions to this system of equations.