When solving this problem, they want us to use substitution. So we're going to look at either of the two equations and try to find a single variable by itself with A1 or -1 coefficient. So the second equation I could solve for Y. If I took the two X to the other side and then I divided 3 by a negative, I'd get Y equaling two X -, 4. So I took the two X to the other side, so negative two X + 4. And then I divided it all through by a negative. So by the substitution method, it now says I'm going to take this equation and I'm going to substitute it into the other. So I get two X + 4 Y equaling -2 instead of that four Y, I'm going to put in what Y equaled, which is 2 X -4. So now we're going to do distribution 2X plus eight X -, 16 equal -2, combine our like terms of X's and take that -16 to the other side. So -2 + 16 is 14. To get X by itself, we're going to divide by 10. So X is 14 tenths. Or if we reduce, A2 comes out of both, so we get 7 fifths. Now once we find our X, we know that Y was two times our X. In this case, the seven fifths minus four 2 * 7 fifths. This two we could think of as over one. So we get 14 fifths, and the four we're going to think of as over 5 S 4 / 1 turns into 20 / 5. So 14 fifths -20 fifths is going to give us -6 fifths. So our solution here is 7 fifths -6 fifths. That tells me those two lines are intersecting. The fact that there's at least one solution means it's consistent, and the fact that there's only one solution tells me that these actually are intersecting. So they're independent lines.