A fruit stand has to decide what to charge for their produce. They need $5 for 1 Apple and 1 orange. They also need $15 for 3 apples and 3 oranges. Put this information into a system of linear equations. Can we find a unique price for an apple and an orange?

No; the system has many solutions. The unique price cannot be found for an apple and an orange

Step-by-step explanation:

Let 'x' be the cost of apple and 'y' be the cost of orange.

x + y = 5

Changing it into slope-intercept form "y = mx + b"

y = 5 - x  or y = -x + 5 >eq(1)

3x + 3y = 15

Lets check whether they are parallel (no solution) or coinciding/overlapping (many solution) by converting the above equation into slope intercept form i.e y = mx + b:

3x + 3y = 15 (simplifying it by taking out common)

3(x + y) =15

x+ y = 15/3

x+y = 5

Changing it into slope-intercept form "y = mx + b"

y = 5 - x  or y = -x + 5> eq(2)

Both the equations are same in form of y=mx + b.  Therefore, both have the same slope -1 and y-intercept of 5.    

If the system has the same slope and y-intercept, then it is coinciding, consistent and dependent. Therefore, we can colclude that, it has infinite solutions.

Ans: No; the system has many solutions. The unique price cannot be found for an apple and an orange