Question

1. Lisa is working with the system of equations x+2y=7 and 2x−5y=5. She multiplies the first equation by 2 and then subtracts the second equation to find 9y=9, telling her that y=1. Lisa then finds that x=5. Thinking about this procedure, Lisa wonders: There are lots of ways I could go about solving this problem. I could add 5 times the first equation and twice the second or I could multiply the first equation by -2 and add the second. I seem to find that there is only one solution to the two equations but I wonder if I will get the same solution if I use a different method? A. What is the answer to Lisa's question? Explain. B. Does the answer to (a) change if we have a system of two equations in two unknowns with no solutions? What if there are infinitely many solutions? 2. Graph (Links to an external site.) the following linear system. What is the solution? y = 2x + 4 y = 3x + 2

Answer 1

A. Yes

B. No

C. No

D. The graph of the equations is attached

x = 2

Explanation:

A. Yes, she will get the same solution

Given the solution is based on the two solutions, the solution will be the same for all algebraic methods used

B. No, the answer in A does not change

A system of two equations in two unknowns with no solution is an inconsistent system of equations and there should be no solutions for all correct algebraic methods used

C. No, the answer in A does not change

If there are infinitely many solutions, there will be infinitely many solutions for all correct algebraic methods used

D. The graph of the equations;

y = 2·x + 4...(1) and y = 3·x + 2.....(2) is attached

Subtracting equation (1) from equation (2), we have;

3·x + 2 - (2·x + 4) = y - y = 0

x - 2 = 0

∴ x = 2

The graphs of the two equations also intersect at x = 2.