 And we need to first rearrange one of our equations so we get either x or y alone. So let's try that. In the bottom equation, or the second equation, let's actually number these. Let's call this equation number one, equation number two. In equation number two, if we subtract two y from both sides, that would leave us with x is equal to negative two y plus two. Now we can take that, take our rearranged equation number two, and plug it into equation number one. For each instance of x, I'm going to take my equation and write that in. So equation number one, again, negative five times x, leave some space, plus three y is equal to twelve. So that was equation one, I'm going to take equation two and plug it in for where x used to be, so negative two y plus two. And now we need to solve for y. Let's go through, well let's distribute first. So we distribute negative five times negative two y is positive ten y, negative five times positive two, so we'd minus ten, plus three y equals twelve. Then go through collect like terms, we've got ten y, and I've got three y, together we'll mix thirteen y, minus ten equals twelve, and then add ten to both sides. Alright, so that leaves us with thirteen y is equal to twenty two, and then divide by thirteen, yeesh, y is twenty two thirteenths, yeah, well we're half done, we haven't yet solved the system, right, for solving a system we need a y and an x. So we can take that value of y, twenty two thirteenths, and plug it into either equation number one or equation number two to solve for x, doesn't matter which since they'll both give us the same answer. I think equation number two is going to be much faster, and in particular if we use equation number two in this rearranged form, it's going to make it a whole lot faster. So let's rewrite that down below, x is negative two y plus two, negative two y plus two, check quick, yeah, sweet. So instead of y, we're actually going to plug in, plug in this value that we computed, twenty two over thirteen. So negative two times twenty two thirteenths, that tells me that x is equal to, well negative two times twenty two is negative forty four thirteenths plus two, and I know that negative forty four over thirteen, and then if I want common denominators, two, well, would be twenty six over thirteen, and that gives me negative forty four plus twenty six makes negative eighteen thirteenths. So that would be my x value. So a complete final answer is an x value, negative eighteen thirteenths, and our y value, twenty two thirteenths.