 In this video, we're going to discover how to solve simultaneous equations by substitution. Simultaneous equations are two or more equations with two or more unknowns. They're called simultaneous because they need to be solved at the same time. We saw how to solve them by elimination in this video. However, elimination doesn't always work, so that means we need to use substitution. We're going to discover how in this video. When we solve simultaneous equations, we may get one solution, like with these linear equations, at 2, 4. Or if a quadratic is involved, we may get two solutions, negative 1, 2 and 2, 5. And we might also get two solutions with a straight line and a circle. Before we start, we need to know what linear equations look like. They are equations with an x and a y in, or an a and a b, but no squared or cubed letters. So let's look at an example of how to solve simultaneous equations by substitution. Start by rearranging the linear equation to become y equals, so y equals x plus 3. We can now substitute this y equals into the nonlinear equation. So in place of the y, we write x plus 3 equals x squared plus 1. Rearrange this to get a quadratic, then factorize and solve it to get x equals negative 1 and x equals 2. Because we have two x values, we need two y values. Substitute the x values into the linear y equals equation. So when x is negative 1, y is 2. And when x is 2, y is 5. So the solutions are negative 1, 2 and 2, 5. As always with maths, we should double check our answers. Substitute the solutions negative 1, 2 and 2, 5 into the nonlinear equation. For negative 1, 2, 2 equals negative 1 squared plus 1. 2 equals 2, which is correct. And the same for 2, 5. Here's one for you to do. I'll leave the steps on screen to help you. Pause the video, find both solutions and click play when you're ready. Did you get 1, 3 and 6, 13? So here's one final one for you to do. This time it's a circle and a linear equation, but it's the exact same process. Pause the video, find both solutions and click play when you're ready. Did you get 2 fifths, 11 fifths and negative 1, negative 2? So there we have solving simultaneous equations by substitution. Take your time with the algebra and always double check your answers. Substitution will always work, whereas elimination won't, which is why some people like to use substitution for any simultaneous equations, even easier linear ones, like this.