Solving System of Equations

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.

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

The cost for renting kayaks at Company A is c = 5h + 20. The cost for renting at Company B is c = 7h + 12. What is the number of rental hours for which the cost will be the same for both companies?

• 4 hours

• 5 hours

• 8 hours

• 16 hours

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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Determine if (4, 1) is a solution for the system of equations.
y = -x + 5
y = 2x - 7

• yes

• no

What is the first step in solving a system by Substitution?

• Make sure both equations are in standard form.

• Make sure at least one equation is solved for one variable.

• Make sure both equations are in slope-intercept form.

• Make sure both equations can be solved.

Solve the system of equations.

• (10, 3)

• (6, 3)

• (15, 3)

• No solution

• Infinite Solution

Solve the system of equations.

• (-23, 4)

• (-4, -3)

• (-2, -4)

• No solution

• Infinite solutions

Solve the system by substitution.
5x + 3y = 7
y = 4

• (4,1)

• (4,-1)

• (1,4)

• (-1,4)

y = -2x + 18
y = 8

• (5, 8)

• (-5, 8)

• (2, 8)

• (-2, 8)