Question

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

Answer 1

Answer:ANSWER: (C.) No; the system has many solutions.

Step-by-step explanation: Cost of an apple: x

Cost of an orange: y

Equation 1:

x + y = 5

Change to slope-intercept form y = mx + b:

y = 5 - x  or y = -x + 5 (Equation 1)

Equation 2:

3x + 3y = 15

Check if they are parallel (no solution) or coinciding/overlapping (many solution) by changing Equation 2 to slope intercept form y = mx + b:

3x + 3y = 15

3y = 15 - 3x

Divide each term by their greatest common factor (GCF) 5:

3y/3 = 15/3 - 3x/3

y = 5 - x  or  y = -x + 5  (Equation 2)

Note that the two equations are the same in simplest form of y=mx + b.  Therefore, they 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. When you graph the two equations, they are overlapping or graphed on the same line. Therefore, it has many or infinite solutions.