1)Solve the system by addition.?

Question:–4x – 5y = –13
x + 2y = 7
2)Solve the system by graphing.
x – y = 2
3x – 3y = 6

3)Graph f(x) = –2x + 2.

4)Graph f(x) = –x – 2.

5)The sum of two numbers is 31. Their difference is 7. What are the two numbers?




Answers:
There's really no way of showing you the solution by graphing on EducationAsk.coms.

5) 12 and 19.
1) Write the two equations one on top of the other, matching the x, y and numeric factors. Pick a number to multiply each term of one equation so that either the x or y term has the same coefficient. Here, you can multiply the second equation by 4, making it 4x+8y=28. Add the two equations together and the x term is zero, so you can solve for y. Plug the y into the second equation, and you get the x value. Voila.

2) Unless you mistyped question 2, it's a trick question. The two equations describe the same line. So do 4x-4y-8 and 5x-5y=10, etc. So the two lines on a graph are the same, and there's no unique solution, which would be where the two lines intersect. There's no intersection here -- or maybe it's better to say the two lines intersect at every point.

3) and 4) are simple. Just choose two different values for x and get the y value (remember that on a graph, f(x) is the y value). In 3), if x is 2, y is -2. That's one point on the graph. If x is -2, y is 6. That's the second point. Draw a line between those points and you have the graph. Same thing in 4.

5) is a system of two equations. x+y=31 and x-y=7. Write them one above the other, add them and the y term drops out. Then you know what x is, and can find y easily.
1) Multiply bottom equation by 4 giving you 4x + 8y = 28. Add this to the top equation and the x terms cancel out leaving you with 3y = 15. Therefore, y = 5. Substitute this value into either equation to get the value of x. Into the bottome equation: x + 2(5) = 7. x = -3.

5) x + y = 31 and x - y = 7. Add equations and the y terms cancel leaving you with 2x = 38. x = 19. Again, substitute this value into either equation to get the y value of 12.

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