Question

Choose the system of equations with the graphical solution shown below.
(image of a graph with 2 lines intersecting at the point(1,-1))

5x – y = 6
12x + 6y = 6

5x + y = –6
12x + 6y = 6

5x – y = 6
12x – 6y = 6

5x + y = –6
12x – 6y = –6

Answer 1

Okay, if they intersect at (1,-1) that means x = 1, y = -1 will satisfy all the equations in the system of equations.

Answer 2

i think its asking what the equations of the two lines would be

Answer 3

The intersection point will be at (1,-1). There is only one set of equations listed where both equations are true for x = 1, y = -1.

Answer 4

ohh okay i got it, its A right?

Answer 5

Let's check:
5(1)-(-1) = 6
5+1 = 6
good so far

12x + 6y = 6
12(1) + 6(-1) = 6
12-6=6
looks good!

Answer 6

Now, they could have made this a trickier problem by having a number of different lines that intersected at (1,-1), but didn't match the graph!

Answer 7

There you wouldn't be able to use a shortcut, and would have to puzzle out which equations matched the graph by computing slope, intercepts, etc.

Answer 8

thank you!

Answer 9

Wouldn't be a bad idea to figure out what those other choices look like, just for practice. The more you do it, the easier it gets.

Answer 10

Here's a tip: you can quickly plot a line by finding the x and y intercepts, marking them, then drawing a line through them. To find the x and y intercepts, just substitute 0 for one variable and solve for the other. For 5x-y = 6, for example, the x intercept (which is where y = 0) is 5x-0 =6, or x = 6/5. You can see if you look at the graph that the line going up to the right crosses the x-axis at x = 6/5. The y intercept (where x=0) is 0-y=6 or y = -6, and sure enough, that line crosses the y-axis at y = -6.