Video: Solving Simultaneous Equations Graphically

Use the shown graph to solve the given simultaneous equations. (𝑥 − 2)² + (𝑦 − 3)² = 16, 𝑦 = 𝑥 + 5.

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Video Transcript

Use the shown graph to solve the simultaneous equations 𝑥 minus two all squared plus 𝑦 minus three all squared equals 16 and 𝑦 equals 𝑥 plus five.

The equation 𝑥 minus two all squared plus 𝑦 minus three all squared equals 16 is a circle with center two, three and radius four. The equation 𝑦 equals 𝑥 plus five is a diagonal line with slope or gradient equal to one and 𝑦-intercept equal to five.

We could solve this problem algebraically. However, we are told to use the graphs. Therefore, the solutions are the points of intersection. The line intersects the circle at two points. They have coordinates two, seven and negative two, three. This means that our solutions are 𝑥 equals two, 𝑦 equals seven and 𝑥 equals negative two, 𝑦 equals three.

We could check these answers by substituting the values into both of the equations: 𝑦 equals 𝑥 plus five and 𝑥 minus two all squared plus 𝑦 minus three all squared is equal to 16.

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