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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

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ujgg

Answer:

Your answer is Division Property of Equality

Step-by-step 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

Answer:

Division property of equality

Step-by-step 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

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