Answer :
Answer:
see the explanation
Step-by-step explanation:
An example of
Part 1) subtraction property of equality
we know that
The subtraction property of equality states that: if we subtract from one side of an equation, we also must subtract from the other side of the equation to keep the equation the same'
Example 1
we have
[tex]x+2y=5[/tex] ----> equation A
subtract 5 both sides
[tex]x+2y-5=5-5[/tex]
[tex]x+2y-5=0[/tex] ----> equation B
so
equation A=equation B -----> by subtraction property of equality
Example 2
we have
[tex]25=25[/tex]
subtract 5 both sides
[tex]25-5=25-5[/tex]
[tex]20=20[/tex] ---> both sides remain equal by subtraction property of equality
Part 2) multiplication property of equality
we know that
The Multiplication Property of Equality states that: if you multiply both sides of an equation by the same number, the sides remain equal
Example 1
[tex]\frac{2}{5} x+y=10[/tex] ----> equation A
Multiply by 5 both sides
[tex]2x+5y=50[/tex] ----> equation B
so
equation A=equation B -----> by multiplication property of equality
Example 2
we have
[tex]30=30[/tex]
Multiply by 4 both sides
[tex]4(30)=4(30)[/tex]
[tex]120=120[/tex] ---> both sides remain equal by multiplication property of equality
Part 3) division property of equality
we know that
The Division Property of Equality states that: if you divide both sides of an equation by the same nonzero number, the sides remain equal
Example 1
[tex]4x+6y=10[/tex] ----> equation A
Divide by 2 both sides
[tex]2x+3y=5[/tex] ----> equation B
so
equation A=equation B -----> by division property of equality
Example 2
we have
[tex]30=30[/tex]
Divide by 3 both sides
[tex]30/3=30/3[/tex]
[tex]10=10[/tex] ---> both sides remain equal by division property of equality