Interpret Systems of Equations

Zendaya runs a farm stand that sells blueberries and grapes. Each pound of blueberries sells for $2.50 and each pound of grapes sells for $1.25. Zendaya made $55 from selling a total of 33 pounds of blueberries and grapes. x + y = 33 2.50x + 1.25y = 55 How many pounds of grapes did she sell? Just type your number answer!

Which ordered pair represents the solution to the equations shown in the graph?

• (0, 6)

• (6, 0)

• (0, 10)

• (10, 0)

Jessica is solving the system of equations shown below. If she graphs this system on a coordinate plane, how could she interpret the solution of this system?

• The system will be parallel.

• The system will be one line.

• The system will intersect at one point.

• The system will intersect at two different points.

Which point satisfies both equations?

y - x = 2

y + 2x = 2

• (0, 2)

• (2, 0)

• (2, 4)

• (-2, 6)

A jar contains only nickels and quarters. The total number of coins in the jar is 15. The total value of the coins is $2.35. Which system of equations represents this situation?

• n + q = 2.35

  .05n + .25q = 15

• n + q = 15

  .5n + .25q = 15

• n + q =15

  .05n + .25q = 2.35

• .05n + q = 15

  n + .25q = 2.35

At which point do the graphs of these equations intersect?

• (0, 4)

• (4, 0)

• The graphs do not intersect.

• The graphs represent the same line

Jan has $100 in her bank account. She adds $15 to her account each month. Maura had $130 in her bank account . She adds $10 to her account each month. A system of equations is used to find how many monthly deposits will be needed for the accounts to have equal balances. Which graph correctly depicts this system of equations and its solution?

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This is a system of equations.

-2x + y = -8

-x + 2y = -4

How many solutions are there for this system of equations?

• 0

• 1

• 2

• an infinite number

The first equation in a system of two equations is x + 4y = 8. If the graph of the second equation does not intersect the graph of the first equation, what could be a second equation for this system?

(HINT: Convert the first equation to slope-intercept form.)

• y = 4x + 1

• y = 1/4x - 2

• y = -4x + 3

• y = -1/4x - 5

What is the solution to system of equations?

• (-16/3, 20)

• (-4/3, 8)

• (-3, 13)

• (0, 4)