Use the graph shown to solve the given simultaneous equations: 𝑦 equals 𝑥 minus four and 𝑦 equals 𝑥 squared minus three 𝑥 minus one.
The solutions to the simultaneous equations are the points of intersection. In this case, the straight line 𝑦 equals 𝑥 minus four and the curve 𝑦 equals 𝑥 squared minus three 𝑥 minus one intersect at two points. One of the points of intersection occurs when 𝑥 equals one and 𝑦 is equal to negative three. The second point of intersection occurs when 𝑥 equals three and 𝑦 equals negative one. This means that the two points or ordered pairs are one, negative three and three, negative one.
We could check these answers by substituting our coordinates into equation one and equation two. For example, negative three is equal to one minus four. In a similar way, negative one is equal to three squared minus three multiplied by three minus one. The initial equations could also have been solved algebraically as well as graphically. This would have given us the same answers: the two ordered pairs one, negative three and three, negative one.