1. Jonas walks at half the pace of his jogging speed. Draw a graph that shows how far he has gone after x minutes.
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2. Which of the following equations have infinitely many solutions?
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
4. Which point represents the solution to the system of linear equations graphed below?
5. Solve the system of linear equations.
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).
|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)|