Question

Question 3(Multiple Choice Worth 1 points)

(04.03 MC)

The following proof shows an equivalent system of equations created from another system of equations. Fill in the missing reason in the proof.


Statements Reasons
2x + 2y = 14
−4x + 6y = 12 Given
2x + 2y = 14
−2x + 3y = 6 ?
Multiplication Property of Equality
Addition Property of Equality
Division Property of Equality
Subtraction Property of Equality

Answer 1

Division property of equality

Explanation:

2x + 2y = 14 -----------(1)

−4x + 6y = 12---------(2) Given

we can divide through the equation equation (2) by 2

The equation becomes;

-2x + 3y = 6 ----------(3) Division property of equality

(4x ÷2 = 2x 6y÷2 = 3y 12÷2=6)

2x + 2y = 14 -----------(1)

-2x + 3y = 6 ----------(3)

To eliminate x variable, we will add equation (1) and equation (3) together

(2 x+ [-2 x] = 2 x-2 x = 0 2 y + 3 y = 5 y 14 + 6=20)

The equations become;

5y = 20

To get the value of y, we divide both-side of the equation by 5

5y/5 = 20/5

y = 5

To find the value of x, we will simply substitute y =5 in equation (1)

2x + 2y = 14

2x + 2(5) = 14

2x + 10 = 14

subtract 10 from both-side of the equation

2x + 10 -10 = 14 -10

2x = 4

Divide both-side of the equation by 2

2x/2 = 4/2

x = 2

x = 2 and y =5

Answer 2

Your answer is Division Property of Equality

Explanation:

It could be Addition Property of Equality, but the second number shows it is actually the division property of equality. Here's my work:

-4x + 6y = 12 Given

(-4x/2) + (6y / 2) = (12/2)

--Simplify--

−2x + 3y = 6

Sidenote: I'm doing the test right now haha