1. 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.
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.
3. 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).
4. 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)
5. 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.