Question

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?

Answer 1

x + y = 5

3x + 3y = 15

Explanation:

let x represent apple and y represent orange

Hence x + y = 5

and 3x + 3y = 15

Solving both equations simutaneously

From first equation, x = 5-y

Substitute x=5-y into the second equation

3(5-y)+3y = 15

y= 0

x = 5-0 = 5

Answer 2

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

Explanation:

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

• If they need $5 for 1 Apple and 1 orange.

x + y = 5

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

y = 5 - x or y = -x + 5 ----->eq(1)

• If they also need $15 for 3 apples and 3 oranges.

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