Question

Anita began solving the system ​ {x+y=8, x−y=2 ​ by writing 2x=10 .

Which property justifies this step?


Division Property of Equality

Multiplication Property of Equality

Addition Property of Equality

Substitution Property of Equality

Answer 1

Option C is correct

Addition property of Equality justifies the step.

Explanation:

Given the system of equation: x+y = 8 and x-y = 2.

Addition Property of Equality: The method of solving systems of linear equations is the addition Property, in which the two equations are added together to eliminate one of the variables.

Adding the equations states that we add the left sides of the two equations together, and we add the right sides together.

Using the addition property in equation: x+y=8 and x-y =2

then,

`(x+y)+(x-y)=8+2` or

`(x+x)+(y-y)` =10

Eliminate the y- variable; we have

2x=10

Therefore, the only property justifies the step is, Addition Property of Equality.

Answer 2

Anita began solving the system ​ {x+y=8, x−y=2 ​ by writing 2x=10 .

x+y=8

x−y=2

When we add both equations , we will get 2x = 10

x+x becomes 2x

+y -y becomes 0

8 + 2 becomes 10

So by adding two equations we got 2x = 10

Hence we say Addition Property of Equality.

Addition Property of Equality means adding both sides of equations.

x terms and y terms are added . then number are added on the right side