The graph of the line with equation \(y=5-x\) is shown.
When the graph of the line with equation \(y=2x-1\) is also drawn on this number plane, what will be the point of intersection of the two lines?
- \((0, 5)\)
- \((1, 2)\)
- \((2, 3)\)
- \((5, 0)\)
Show Worked Solution
\(\text{Method 1: Graphically}\)
\(\text{From graph, intersection is at} (2,3)\)
\(\text{Method 2: Algebraically}\)
| \(y\) | \(=5-x\) | \(…\ (1)\) |
| \(y\) | \(=2x-1\) | \(…\ (2)\) |
\(\text{Substitute (2) into (1)}\)
| \(2x-1\) | \(=5-x\) |
| \(3x\) | \(=6\) |
| \(x\) | \(=2\) |
\(\text{When}\ \ x=2,\ y=5-2=3\)
\(\Rightarrow C\)
