Solving systems of equations graphicallyIB MYP Maths Extended: Flashcards

What these 12 flashcards ask

What does the intersection of two graphs give?
How do you check a solution of simultaneous equations?
Solve y=x and y=6-x.
What do you read from the graphs to solve f(x)=g(x)?
How many intersections can a line and a parabola have?
What does it mean if two lines are parallel?
What if both equations describe the same line?
Solve x^2=x+6 using graphs of y=x^2 and y=x+6.
What is the gradient of y=-x+7 and its y-intercept?
Why use graphing technology?
Where do y=2x+1 and y=-x+7 meet?
In a real problem, what does the intersection show?

Exam questions on Solving systems of equations graphically

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
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
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

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).