Question

If you have the system below, what would you multiply the second equation by to eliminate the "x" variable?

3x−2y=3
x+4y=5

a) Multiply by 3
b) Multiply by -3
c) Multiply by 2
d) Multiply by -2

Answer 1

To eliminate the "x" variable in a system of equations, you can multiply the second equation by -3, which will result in the new equation -3x - 12y = -15. Adding this to the first equation will eliminate the x variable, allowing you to solve for y.

Step-by-step explanation:

To eliminate the "x" variable from the equations 3x - 2y = 3 and x + 4y = 5, we need to multiply the second equation by a number that will result in the coefficient of x being the opposite of the coefficient of x in the first equation. In this case, we can multiply the second equation by -3. This will give us a new equation: -3x - 12y = -15. Adding this new equation to the first equation will eliminate the x variable:

• 3x - 2y = 3
• -3x - 12y = -15 (this is the second equation multiplied by -3)

By doing this, you will have the following system:

• 3x - 2y = 3
• -3x - 12y = -15

When you add these two equations together, the x variable will be eliminated:

• (3x - 3x) - (2y + 12y) = 3 - 15
• 0x - 14y = -12

Now you can solve for y by dividing both sides by -14.