Question

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

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.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To solve the system of equations using elimination with multiplication, we need to multiply one or both of the equations by a number so that the coefficients of one of the variables are the same, but with opposite signs.

Let's start by multiplying the second equation by 2 to make the coefficient of x in both equations opposite:

2 * (-2x + 4y) = 2 * 30
-4x + 8y = 60

Now we have the following system of equations:

4x - 6y = -48
-4x + 8y = 60

Next, we add the equations together to eliminate x:

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

Simplifying, we have:

-6y + 8y = 12
2y = 12

Now, solve for y by dividing both sides of the equation by 2:

2y / 2 = 12 / 2
y = 6

Now that we have the value of y, we can substitute it back into either of the original equations to solve for x. Let's use the first equation:

4x - 6(6) = -48
4x - 36 = -48

Next, add 36 to both sides of the equation:

4x - 36 + 36 = -48 + 36
4x = -12

Finally, divide both sides of the equation by 4 to solve for x:

4x / 4 = -12 / 4
x = -3

Therefore, the solution to the system of equations is x = -3 and y = 6.

Answer 3

[AI-generated answer — Explain Bot]

To solve the system of equations using elimination with multiplication, we need to manipulate one or both of the equations so that when they are added or subtracted, one of the variables will be eliminated. Here's how to do it:

1. Multiply one or both of the equations by a constant to create equal coefficients for one of the variables. In this case, we'll multiply the second equation by 2 to make the coefficients of x opposite in sign.

Equation 1: 4x - 6y = -48
Equation 2 (after multiplying by 2): -4x + 8y = 60

2. Now, add the equations together to eliminate the x variable.

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

Simplifying and combining like terms, we get:
-6y + 8y = 12

2y = 12

Divide both sides of the equation by 2 to solve for y:
y = 6

3. Substitute the value of y back into either of the original equations to solve for x. Let's use Equation 1.

4x - 6(6) = -48

4x - 36 = -48

Add 36 to both sides to isolate the x variable:
4x = -48 + 36

4x = -12

Divide both sides of the equation by 4 to solve for x:
x = -3

Therefore, the solution to the system of equations is x = -3 and y = 6.