To solve the system of equations using elimination with multiplication, we want to eliminate one of the variables by multiplying one or both of the equations by a constant so that the coefficients of one of the variables are equal in both equations.
To eliminate the variable x, we need to multiply the second equation by a constant that will make the coefficients of x in both equations equal. The coefficients of x in the equations are already opposite, so we don't need to multiply any equation to eliminate x.
Let's write the equations again:
4x - 6y = -48 (Equation 1)
-2x + 4y = 30 (Equation 2)
Now, let's add the two equations together:
(Equation 1) + (Equation 2):
4x - 6y + (-2x + 4y) = -48 + 30
Simplifying:
2x - 2y = -18
Now we have a new equation with only one variable. Let's solve it:
2x - 2y = -18
Divide both sides of the equation by 2:
x - y = -9
We have eliminated the variable x. Now let's solve for y:
x - y = -9
y = x + 9
Now we have an equation for y in terms of x.
The solution to the system of equations is x = any real number and y = x + 9.
Solve the system of two equations using elimination with multiplication. 4x−6y=−48 −2x+4y=30 (1 point)
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