Simultaneous equationsAQA A-Level Maths: Mind map

Exam questions on Simultaneous equations

1. The straight lines $x+2y=7$ and $3x-y=7$ meet at the point $P$. The first line crosses the $y$-axis at $A$ and the second line crosses the $y$-axis at $B$.
   Find the area of triangle $ABP$.2 marks
2. The line $y=x+1$ and the curve $y=x^{2}-5$ intersect at two points.
   Find the exact distance between the two points of intersection.2 marks
3. The line $2x+y=k$, where $k$ is a constant, and the curve $C$ with equation $x^{2}+y^{2}=20$.
   Show that the $x$-coordinates of any points of intersection satisfy $5x^2-4kx+k^2-20=0$.3 marks