Question

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

Answer 1

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.