Afruit stand has to decide what to charge for their produce. they decide to charge \$5.30$5.30 for 11 apple and 11 orange. they also plan to charge \$14$14 for 22 apples and 22 oranges. we put this information into a system of linear equations. can we find a unique price for an apple and an orange?

No, we can not find a unique price for an apple and an orange.

Step-by-step explanation:

Let x be the price of each apple and y be the price of each orange.

We have been given that a fruit stand charge $5.30 for 1 apple and 1 orange. We can represent this information as:

We are also told that they plan to charge $14 for 2 apples and 2 oranges. We can represent this information as:

Upon dividing equation (2) by 2 we will get,

Upon converting our equations into slope-intercept form we will get,

We can see that slope for both lines in -1, but both lines have different y-intercept, so these lines are parallel lines.

Since parallel lines do not intersect, therefore, we can not find a unique price for an apple and an orange.

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

answer: sherk

step-by-step explanation:

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