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