Question

Consider the linear equation: 6x + 4y = -12 If x = -4, then y = . If y = 0, then x =

Answer 1

Given 6x+4y=-12, we want to find y when x=-4 and x when y=0. First, we can translate the equation into slope-intercept form for simplified solving:

We will translate from ax+by=c to y=mx+b and as long as we use the proper algebraic steps, the equations will be equal, giving us the same information.

Subtract 6x from both sides:

4y=-6x-12

Divide by 4 on both sides to solve for y:

y=-6/4x-12/4

Simplify any fractions:

y=-3/2x-3

Now, we have the same equation in a simper form, so let’s plug in the values.

If x=-4, then:

y=-3/2(-4)-3

*We just substituted x=-4 in the function.

Use PEMDAS to evaluate:

y=12/2-3

y=6-3

y=3

So, the solution is (-4, 3).

If y=0, then:

(0)=-3/2x-3

*We substituted in y=0 into the function and will solve for x.

Combine like terms with inverse operations: add 3 to both sides

3=-3/2x

Take the reciprocal of any fractions in both sides to cancel them out and isolate x:

(-2/3)3=x

-2=x ; x=-2

So, the solution is (0, -2)

Answer 2

If x = -4, then y = 3

If y = 0, then x = -2

Explanation:

For each of these, we will substitute the given value and solve for the unknown variable. To solve, we will use inverse operations.

If x = -4;

6x + 4y = -12

6(-4) + 4y = -12

-24 + 4y = -12

4y = 12

y = 3

If y = 0;

6x + 4y = -12

6x + 4(0) = -12

6x = -12

x = -2