WEBVTT
00:00:00.640 --> 00:00:15.000
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.
00:00:15.800 --> 00:00:27.800
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.
00:00:28.320 --> 00:00:38.120
The equation 𝑦 equals 𝑥 plus five is a diagonal line with slope or gradient equal to one and 𝑦-intercept equal to five.
00:00:39.040 --> 00:00:41.040
We could solve this problem algebraically.
00:00:41.400 --> 00:00:44.280
However, we are told to use the graphs.
00:00:44.680 --> 00:00:48.040
Therefore, the solutions are the points of intersection.
00:00:48.800 --> 00:00:51.600
The line intersects the circle at two points.
00:00:52.120 --> 00:00:56.800
They have coordinates two, seven and negative two, three.
00:00:57.560 --> 00:01:06.200
This means that our solutions are 𝑥 equals two, 𝑦 equals seven and 𝑥 equals negative two, 𝑦 equals three.
00:01:06.880 --> 00:01:22.160
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.