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Which ordered pair is a solution to the system of linear equations 1/2x-3/4y=11/60 and 2/5x+1/6y=3/10

Which ordered pair is a solution to the system of linear equations 1/2x-3/4y=11/60 and-example-1
User Jboxxx
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2 Answers

1 vote

Answer:

d

Explanation:

2/3, 1/5

User Oskar Berggren
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6 votes

ANSWER


( (2)/(3) , (1)/(5) )

EXPLANATION

The first equation is


(1)/(2) x - (3)/(4) y = (11)/(60) ...(1)

The second equation is


(2)/(5) x + (1)/(6) y = (3)/(10) ...(2)

We want to eliminate y, so we multiply the first equation by


(4)/(5)


(4)/(5) * (1)/(2) x - (4)/(5) * (3)/(4) y = (11)/(60) * (4)/(5)


(2)/(5) x - (3)/(5) y = (11)/(75) ...(3)

We now subtract equation (3) from (2)


((2)/(3) x - (2)/(3) x )+ ( (1)/(6) y - - (3)/(5)y ) =( (3)/(10) - (11)/(75) )


(1)/(6) y + (3)/(5)y =(3)/(10) - (11)/(75)


(23)/(30)y = (23)/(150)

Multiply both sides by


(30)/(23)


\implies \: (30)/(23) * (23)/(30)y= (23)/(150) * (30)/(23)


\implies \: y = (1)/(5)

Substitute into the first equation to solve for x .


(1)/(2) x - (3)/(4) * (1)/(5) = (11)/(60)

Multiply to obtain


(1)/(2) x - (3)/(20) = (11)/(60)


(1)/(2) x = (11)/(60) + (3)/(20)


(1)/(2) x = (1)/(3)

Multiply both sides by 2.


2 * (1)/(2) x =2 * (1)/(3)


x = (2)/(3)

The solution is


( (2)/(3) , (1)/(5) )

User Shijinmon Pallikal
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