Solving Systems by Elimination

Question

Lin and Priya were working on solving this system of equations.

Lin's first move is to multiply the first equation by 3. 

Priya's first move is to multiply the second equation by 2.

1. Explain why either move creates a new equation with the same solutions as the original equation.

Answer 1

If you add / subtract the same value to both sides of an equation, or you multiply / divide both sides of an equation by the same value, then the resulting equation is equivalent (i.e. has the same solutions). This is similar to multiplying (or dividing) the top and bottom of a fraction by the same number to get an equivalent fraction.

for (1/3)x + 2y = 4 Lin multiplies both sides by 3 to give x + 6y = 12

Lin's strategy is to have two equation with one x, and subtract to eliminate the x term.

for x + y = -3 Priya multiplies both side by 2 to give 2x + 2y = -6

Priya's strategy is to have two equations with 2y, and subtract to eliminate the y term.

Answer 2

Multiplicative Property of Equality