A: 5x - 2y = 10
b: 4x + 3y = 7
to solve this system of equations by addition, what could you multiply each equation by to cancel out the x-variable a) multiply a by 3 and b by 2
b) multiply a by 4 and b by 5
c) multiply a by -3 and b by 2
d) multiply a by -4 and b by 5

The answer is D) you could multiply A by -4 and B by 5,

This choice would help you cancel out the x variable so that you could solve for the y. To see this, multiply the x terms by the given amounts.

Equation A (just the x)

5x > multiply by the -4 above

5x * -4 = -20x

Equation B (just the x)

4x > multiply by the 5 above

4x * 5 = 20x

Since -20x and 20x cancel when adding, these are the numbers that you are looking for.

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.