Question

The graph of a system of equations will intersect at more than 1 point.

Always

Sometimes

Never

Answer 1

I'll give you a hint, where do the following systems of equations intersect?

A:\[3x-4y=7\]\[12x-16y=28\]

B:\[x-y=2\]\[x+y=4\]

Answer 2

how can you tell if they intersect?

Answer 3

Do you know how to solve systems of equations? If not I can teach you quickly.

Answer 4

please teach me lol

Answer 5

Ok, there are two ways of solving systems of equations.

The first is called substitution. In one of the equations, you solve for one variable. Then, in the second equation, in place of that variable you substitute in what it equals. As an example:\[x-y=2\]\[x+y=4\]I will solve the first equation for x:\[x=y+2\]Now, in the second equation, I can replace every instance of x with y+2:\[x+y=y+2+y=4\]Then I just solve for y.\[2y+2=4\]\[2y=2\]\[y=1\]And now that I know that y=1, I can use that to find x. I'll go back to the first equation that I solved for x, and just put 1 in where y is:\[x=y+2=1+2=3\]So we know that the system of equations intersects at (3,1)


The other method is elimination. In this method, multiply one of the equations by a constant, and then add or subtract it from the other one in such a way to eliminate one of the variables. Example:\[x-y=2\]\[x+y=4\]If I add the two equations together, the ys will cancel out:\[x-y+x+y=2+4\]\[2x=6\]\[x=3\]Then I can take that value of x and, using either equation, find y:\[x+y=4\]\[3+y=4\]\[y=1\]So again we find that the system intersects at (3,1).


Does all that make sense?

Answer 6

yes it does :))

Answer 7

is the answer B?

Answer 8

Yes, sorry I disappeared.