**1. Jonas walks at half the pace of his jogging speed. Draw a graph that shows how far he has gone after x minutes.**

**2. Which of the following equations have infinitely many solutions?**

A. 3(2x-5)=6x-15

B. 4x-8=12

C. 5=10x-15

D. 7x=2x+35

**3. John was given the following equation and asked to solve for x. 2/3 x-1=5. His solution is shown below. Circle the step where he made a mistake and then choose the answer choice that fixes it.**

A. 2/3 x=8

B. 2/3 x=6

C. x=8

D. x=2/((2/3))

**4. Which point represents the solution to the system of linear equations graphed below?**

A. (0,0)

B. (0,-3)

c. (-2,-1)

D. (-3,0)

**5. Solve the system of linear equations. **

A.(0,5)

B.(-2,1)

C.(1,2)

D.(-3,-4)

## Answers

**1.** If Jonas walks at half the pace he jogs then he will only cover half on the distance when walking. The line is shown below.

**2. A:** A is the only one that has infinitely many solutions because when the 3 is distributed across the parentheses, the resulting equation is 6x-15=6x-15. Because each side of the equation is identical to the other side, any value of x will make a true statement, so there are infinitely many solutions.

**3. B.** The answer that John gave was:

However, he messed up on the second step when he moved the -1 across it should have become a positive 1. That step should be 2/3 x=6.

**4. C: **Given the graph of a system of linear equations, the solution is the point of intersection of the two lines. In this graph, the two lines intersect at (-2,-1).

**5. A:**

3x-2(2x+5)=-10 | Substitute the expression for y into the other equation |

3x-4x-10=-10 | Distribute the -2 across the parentheses |

-x-10=-10 | Combine like terms |

-x=0 | Add 10 to both sides |

x=0 | Divide by -1 |

y=2(0)+5=5 | Substitute the value of x into the original equation and simplify. |

(0,5) | Write your final answer as an ordered pair (x,y) |

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by Enoch Morrison | Last Updated: January 9, 2019