Lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8.50. Ari buys 3 pounds of apples and 2 pounds of bananas for a total of $5.25. This system of equations represents the situation, where x is the cost per
pound of apples, and y is the cost per pound of bananas.
5x + 3y = 8.5
3x + 2y = 5.25
If you multiply the first equation by 2, what number should you multiply the second equation by in order to eliminate
the y terms when making a linear combination?
Complete the multiplication and add the equations. What is the result?
What is the price per pound of apples? $
What is the price per pound of bananas?

In order to eliminate y term from the system of equations we multiply equation 2 by -3.

The price per pound of apple is 1.25 dollars and the price per pound of bananas is 0.75 dollars.

Given equations,

.........(1)

.......(2)

Here x is the cost per  pound of apples, and y is the cost per pound of bananas.

According to the question, multiply the first equation by 2, we get

.....(3)

So, in order to eliminate y term from the system of equations we multiply equation 2 by -3, we get

.....(4)

Now Adding (3) and (4) equation, we get

Putting the above value of x in equation 3 we get,

Hence the price per pound of apple is 1.25 dollars and the price per pound of bananas is 0.75 dollars.

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price per pound of apple = $1.25

price per pound of banana = $0.75

Step-by-step explanation:

Your first question is what value should you multiply the second equation by in order to eliminate the y terms.

The number should be 3.  Let us multiply the first equation by 2 and the second equation by 3 and see how y will be eliminated.

10x + 6y = 17(i)

9x + 6y = 15.75(ii)

10x - 9x  = x

6y - 6y = 0

17 - 15.75 = 1.25

x = 1.25

let us find y

10x + 6y = 17(i)

10(1.25) + 6y = 17

12.5  + 6y = 17

6y = 17 - 12.5

6y = 4.5

divide both  sides by 6

y = 4.5/6

y = 0.75

1. 3. can also be expressed as (22/7)

2. -4.5

3. 3.6

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