Solving systems of equations graphicallyIB MYP Maths Extended: Mind map

Exam questions on Solving systems of equations graphically

1. Two straight lines are drawn on the same axes: $y = 2x + 1$ and $y = -x + 7$.
   Use algebra to find the coordinates of the point where the two lines meet.2 marks
2. Tank A holds $50$ litres of water and is filled at $5$ litres per minute, so after $t$ minutes it holds $V = 50 + 5t$ litres. Tank B holds $20$ litres and is filled at $8$ litres per minute, so after $t$ minutes it holds $V = 20 + 8t$ litres.
   Find the time at which the two tanks hold the same volume of water, and state that volume.2 marks
3. The graphs of $f(x) = x^2 - 2$ and $g(x) = x + 4$ are drawn on the same axes.
   Show that the $x$-coordinates of the points where the two graphs meet satisfy $x^2-x-6=0$, and solve this equation.3 marks