Question

Consider the following system of equations.

2x-y=12 -3x-5y=-5

The steps for solving the given system of equations are shown below.
step one -5(2x-y=12) -3x-5y=-5
step two -10x+5y=-5
step 3 -13x=-65
step 4
x=5
step 5
2(5)-y=12
step 6
y=-2

solution (5,-2) Select the correct statement about step 3.
A. When the equations -10x + 5y = -60 and -3x − 5y = -5 are added together, a third linear equation, -13x = -65, is formed, and it has a different solution from the original equations.
B. When the equation -3x − 5y = -5 is subtracted from -10x + 5y = -60, a third linear equation, -13x = -65, is formed, and it has a different solution from the original equations.
C. When the equations -10x + 5y = -60 and -3x − 5y = -5 are added together, a third linear equation, -13x = -65, is formed, and it shares a common solution with the original equations.
D. When the equation -3x − 5y = -5 is subtracted from -10x + 5y = -60, a third linear equation, -13x = -65, is formed, and it shares a common solution with the original equations. Reset Next

Answer 1

C

Explanation:

Answer 2

C. When the equations -10x + 5y = -60 and -3x − 5y = -5 are added together, a third linear equation, -13x = -65, is formed, and it shares a common solution with the original equations.

Explanation:

2x-y=12

-3x-5y=-5

multiply the first equation by -5

-10x +5y = -60

add the 2 equations together

-3x-5y=-5

-10x +5y = -60

-------------------------

-13x = -65

We use the addition property of equality which says adding the same thing to both sides, doesn't change the equation, so we will get the same answer as the original equation