 In this video we're going to discover what simultaneous equations are and how to solve them. Simultaneous equations are two or more equations with two or more unknowns. They're called simultaneous because they need to be solved at the exact same time. There are three different methods we can use to solve simultaneous equations. We can solve them graphically and see where they cross each other. But this is really slow and actually only works if they cross at an exact point. The other two methods involve solving algebraically by elimination or by substitution. In this video we're going to discover how to use elimination. Solving simultaneous equations by elimination only works when we have linear equations. So equations that look like this, with an x and a y, no x-squads or y-squads. Let's get started with an example. We start by lining the two equations up, one on top of the other, with the x's, the y's and the numbers all lined up. We now need to eliminate either our x's or our y's. Hence the method is called elimination. This means that we need to have an equal number of one of those letters. Luckily for us in this example there are two y's already in both equations. So we can eliminate these straight away. We're going to either add or subtract the equations. Looking back at our matching two y's, if the signs are the same we subtract. Just remember same signs subtract s s s. Here the signs are different. This one is plus two y and the other is minus two y. So we add the two equations. Five x add three x is eight x. Plus two y add minus two y is zero. So we've eliminated the y's. Eighteen add minus two is sixteen. So eight x equals sixteen. Solve for x, so divide both sides by eight and x is two. Now we need to find the corresponding y value. Choose either one of the starting equations. So I'm going to choose the top one. Substitute x is two into this equation. Five multiplied by two add two y equals eighteen. And solve the equation. Two y equals eight y equals four. So when x is two y is four. This is the solution to these simultaneous equations. It's then really important to check our answers. So we need to substitute two four back into the other equation. Into this equation. Three times two minus two times four equals negative two. So six minus eight is negative two, which is correct. That's all there is to it, much faster than having to plot the graphs. Let's have a look at another example. So we start by lining the two equations up. Which means we'll need to rearrange the bottom equation to become five x plus three y equals 11. Now to eliminate either our x's or our y's. We need to have an equal number of either x's or y's, which we don't have. So we're going to have to multiply the whole equations to match up one of these letters. I'm going to multiply everything in the top equation by three to get six y. And everything in the bottom equation by two to also get six y. Maybe you wanted to match up your x's instead. So you could have multiplied the top equation all by five. And the bottom equation all by three. It makes no difference. You'll still get the same answers. So back to having six y in both. Now to eliminate. Remember, same sign subtract. Both are plus six y. So we subtract the equations. Nine x minus ten x is minus one x. Plus six y minus six y is zero. Eighteen minus twenty two is minus four. Solve for x means x is four. Can you now find the corresponding y value by substituting x is four into one of the original equations? Pause the video, find y and click play when you're ready. Did you get y is negative three and did you check four negative three was correct? So here's one for you to do. I'll leave the steps on screen to help you. Pause the video, solve for x and y and click play when you're ready. Did you get negative one two? So there we have solving simultaneous equations by elimination. You just need to remember same sign subtract s s s. This works perfectly for linear equations, but won't work if there's a quadratic involved for example. So that we have to use substitution. Watch this video to discover how.