Use the shown graph to solve the given simultaneous equations: 𝑦 equals 𝑥 minus one and 𝑦 equals 𝑥 squared plus two 𝑥 minus three.
The equation 𝑦 equals 𝑥 minus one is a diagonal line with slope or gradient equal to one and intercept equal to negative one. The equation 𝑦 equals 𝑥 squared plus two 𝑥 minus three is a U-shaped graph with intercept negative three.
We could solve this problem algebraically. However, we have been asked to solve it using the graphs. Therefore, the solutions are the points of intersection. There are two points of intersection on the graph. Their coordinates are one, zero and negative two, negative three.
This means that we have two solutions: 𝑥 equals one, and 𝑦 equals zero; and 𝑥 equals negative two, 𝑦 equals negative three. We could check these solutions by substituting the values back into either of the two equations: 𝑦 equals 𝑥 minus one or 𝑦 equals 𝑥 squared plus two 𝑥 minus three.