Question

Pete began solving the system ​ {x+3y=132x−y=−2 ​ by rewriting the system as {x+3y=136x−3y=−6 .

Which property justifies this step?

a. addition property of equality

b. subtraction property of equality

c. substitution property of equality

d. multiplication property of equality

Answer 1

Pete used multiplication property of equality

D is correct

Explanation:

Pete began solving the system of equation.

x+3y=13

2x-y=-2

Pete re-write the system of equation

x+3y=13

6x-3y=-6

If we see both system of equation.

Equation 1 is same in both case. No change in equation.

Equation 2: 2x-y=-2 changes to 6x-3y=-6

each coefficient of equation changes to 3 times.

So, Pete multiply each term of 2nd equation by 3.

Hence, Pete use multiplication property of equality

Answer 2

The answer would be multiplication property of equality. For this property, it states that when you multiply one side of the equation, the other should be multiplied as with the same factor for the equation to be still the same. For this case 3 was multiplied to both.