 So let's try to solve the system of equations 2x plus 7y equals 3, 3x plus 4y equals negative 2. So we could solve this using substitution. So first we want to solve one of the equations for one of the variables. So let's pick this first equation, 2x plus 7y equals 3, and solve it for, well, I don't know, how about x? So our left-hand side is a sum. So to get rid of a sum, we need to subtract. Let's subtract 7y from both sides. So now we have a 2x equal 3 minus 7y, and our left-hand side is a product, 2 times x. So to get rid of a product, we'll divide. So over on the left-hand side we have a common factor of 2, which we can remove, and over on the right-hand side we have this rational expression. So solving the first equation for x gives us x equals 3 minus 7y over 2. Equals means replaceable, so we can replace this in our second equation and solve for y. And we get this rather nightmarish expression, which we have to then solve for y, and we ask ourselves, what were we thinking when we tried to solve this by substitution? And at this point, if you're me, we're going to say, we really don't want to deal with this mess of fractions, so let's solve this a different way. So we can use the addition method. So here we want to look at the coefficients of a variable. Again, how about x? And we'll multiply each equation by the coefficient of x in the other one, changing one of the sides. So our first equation, our coefficient of x in the other one is 3, so let's multiply our first equation by 3. So we'll multiply both sides of our equation by 3, we'll expand, and get the equation 6x plus 21y equals 9. So our second equation, while our coefficient of x in the other equation is 2, so we'll multiply our second equation by minus 2. So we'll take our second equation and multiply both sides by minus 2, we'll expand, and get the equation minus 6x minus 8y equals 4. And that gives me two equivalent equations where our coefficient of x are equal but opposite. So we can add the two equations together. That gives us 13y equals 13, and our left-hand side is a product, so we'll divide by 13 to get y equals 1. And if it's not written down, it didn't happen, so we might want to summarize what we did. So the first time through we multiplied by the coefficients on x, well let's multiply by our coefficients on y. So we'll take our first equation and multiply it by the coefficient on y in the other equation, so we'll multiply the first equation by 4, which gives us 8x plus 28y equals 12. Our second equation will multiply by negative 7, the negative of the coefficient of y in the first equation, and that gives us minus 21x minus 28y equals 14. We'll add our two equations together. That gives us minus 13x equals 26. Our left-hand side is a product, minus 13 times x, so we'll divide, and we'll get x equals negative 2 as our solution. Thank you.