Solve the system of two equations using elimination with multiplication. 4x-6y=-48 and -2x+4y=30
To solve the system of equations using elimination with multiplication, we need to eliminate one variable by multiplying at least one of the equations by a constant so that the coefficients of that variable will cancel out when the equations are added or subtracted.
Let's start by eliminating the variable "x".
To do this, we multiply the first equation by 2 and the second equation by 4.
(2)(4x-6y) = (2)(-48)
4(2x-3y) = 4(30)
This simplifies to:
8x - 12y = -96
8x - 12y = 120
Now, we can subtract the equation (8x - 12y = 120) from the equation (8x - 12y = -96):
(8x - 12y) - (8x - 12y) = 120 - (-96)
This simplifies to:
0 = 216
This equation is not possible since 0 is not equal to 216.
Therefore, the system of equations is inconsistent and has no solution.