Question

Noah and Lin are solving this system: 12x - 9y = 150. Noah multiplies the first equation by 12 and the second equation by 8, which gives: 96x - 72y = 1,200. What are the smallest whole-number factors by which you can multiply the equations in order to eliminate x?

Answer 1

To eliminate x in the given equation, 12x - 9y = 150, use the smallest whole-number factors which would be multiplying the equation by -1 to get -12x + 9y = -150.

Step-by-step explanation:

The goal is to find the smallest whole-number factors by which you can multiply the equations to eliminate x. To do this, you can use the coefficients of x in the equation to determine these factors. Since we have the equation 12x - 9y = 150, we'd like factors of 12 for each equation that will result in the same coefficient with opposite signs for x when multiplied.

Let's take the coefficients of x in the equation (which is 12) and list its multiples: 12, 24, 36, 48, and so on. The smallest multiple of 12 that we can use to get opposite coefficients would be 12 itself. So, we would multiply the equation by -1 to get -12x + 9y = -150 (since we want the signs to be opposite to eliminate x).