14.3 Solving simultaneous equations graphically — Practise

1. For $y=2x+1$ and $y=-x+7$, find the intersection.

Answer: $x=2$, $y=5$

2. For $y=x-2$ and $y=-2x+7$, find the intersection.

Answer: $x=3$, $y=1$

3. For $y=3x-4$ and $y=x+2$, find the intersection.

Answer: $x=3$, $y=5$

4. For $y=-x+4$ and $y=2x-5$, find the intersection.

Answer: $x=3$, $y=1$

5. For $y=0.5x+2$ and $y=-x+8$, find the intersection.

Answer: $x=4$, $y=4$

6. For $y=4-x$ and $y=2x-5$, find the intersection.

Answer: $x=3$, $y=1$

7. For $y=2x-6$ and $y=-x+3$, find the intersection.

Answer: $x=3$, $y=0$

8. The lines $y=x+1$ and $y=5-x$ cross. State the coordinates of the cros

Answer: $x=2$, $y=3$

9. Explain why the intersection of $y=2x+1$ and $y=-x+7$ solves both equa

Answer: Both equations give $y=5$ when $x=2$, so the point $(2,5)$ lies on both graphs.

10. For $y=3x-2$ and $y=x+4$, find the intersection and the gradient of ea

Answer: Intersection $(3,7)$; gradients are $3$ and $1$.