Question

Which properties justify the steps taken to solve the system?

{3x−4y=92x+8y=6

Drag the answers into the boxes to match each step.



6x−8y=18, 2x+8y=6
8x = 24
x = 3
3(3)−4y=9
9−4y=9
−4y=0
y = 0

Answer 1

Here it is nice and straight forward for you..

Multiplication property of equality

Addition property of equality

Division property of equality

Substitution property of equality

Simplify

Subtraction property of equality

Division property of equality

Answer 2

Multiplication property of equality:

If a = b then,
`a * c = b * c`

Addition property of equality:

If a = b then;
`a+c = b+c`

Subtraction property of equality:

If a = b then;
`a-c = b-c`

Division property of equality:

If a = b then;
`(a)/(c) = (b)/(c)`

Substitution Property of equality:

if a = b then a can be substituted in b , and b can be substituted in a.

Given the system of equation:

`3x-4y=9` .....[1]

`2x+8y = 6` ......[2]

Using multiplication property of equality

Multiply by 2 in equation [1] both sides we get;

`6x-8y=18` .....[3]

Using addition property of equality:

Add equation [2] and [3] to eliminate y we have;

`8x = 24`

Using Division property of equality:

Divide by 8 to both sides of an equation we have;

x = 3

Using substitution property of equality:

Substitute the value of x in equation [1] we have;

`3(3)-4y =9`

9-4y = 9

Using subtraction property of equality:

Subtract 9 from both sides we get;

-4y = 0

Divide by 4 to both sides we get;

y = 0