Solve the  equation for y   3x + 4y + 12 = 0 G= [-4;4] X Z

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dwbettine eNotes educator| Certified Educator

If starting with 3x + 4y + 12 = 0, then isolate the term with the variable in which you are interested. So, subtract 3x from both sides, then subtract 12 from both sides. This results in the equation:

4y = -3x + 12. Next, divide both sides (all terms) by 4.

The result is: y = (-3/4)x -3.

You have now solved the equation for y in terms of x, which means the variable x is still in the solution. This is the slope-intercept form of the equation. The y-intercept is -3, which means the linear function crosses the y axis at y = -3.

You can also solve this problem using the cover-up method! Since the origial equation is in standard form (ax + by + c = 0) , you can simple move the term without a variable attached to the other side of the equation. In this equation, subtract 12 from both sides. The result is now 3x + 4y = -12.

To solve for the y-intercpet, cover up the term with the x variable in it, then solve for y. So you would have 4y = -12. Solving for y yields y = -3. To solve for x, cover up the term with the y variable in it, which leaves 3x = -12. Solving for x yields x = -4.

Therefore, the y-intercept is at y = -3 or (0, -3) and the x-intercept is at x = -4, or (-4, 0).

sciencesolve eNotes educator| Certified Educator

Let 3x to the left side.

3x = -4y - 12

Divide by 3 => x = (-4/3)*y - 4

Solve the equation for y => (-4/3)*y - 4 = 0

Add 4 both sides => (-4/3)*y = 4

y = 4/(-4/3) => y = -(4*3)/4 => y = -3

The solution of the equation is integer, therefore it belongs to Z. The solution of the equation is in the interval [-4;4].

ANSWER: The solution of the equation is y = -3.

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