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) |