Solve the system of equations using elimination with multiplication
4x-6y= -48
-2x+4y= 30
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To solve the system of linear equations using the elimination method, we try to eliminate one of the variables by making the coefficients of that variable in both equations the same with opposite signs. Let's start by expressing both equations:
1) 4x - 6y = -48
2) -2x + 4y = 30
To eliminate one of the variables, we can multiply the second equation by 2 to make the coefficients of x in both equations have the same magnitude:
2 * (-2x + 4y) = 2 * 30
-4x + 8y = 60
Now, let's rewrite the system with the new second equation:
1) 4x - 6y = -48
2) -4x + 8y = 60
Now we can add the two equations together to eliminate the x variable:
(4x - 6y) + (-4x + 8y) = -48 + 60
4x - 4x - 6y + 8y = 12
0x + 2y = 12
Now we simplify the equation:
2y = 12
Next, we divide both sides by 2 to solve for y:
y = 12 / 2
y = 6
Now that we have the value of y, let's substitute it into one of the original equations to solve for x. We can use the first equation for that:
4x - 6y = -48
4x - 6(6) = -48
4x - 36 = -48
Now add 36 to both sides:
4x = -48 + 36
4x = -12
Finally, divide by 4 to solve for x:
x = -12 / 4
x = -3
So, the solution to the system of equations is:
(x, y) = (-3, 6)