Simultaneous Equations
Understand that two linear equations can be solved simultaneously by finding the point where their graphs intersect, and interpret this graphically and algebraically as the pair of values satisfying both equations
What a learner can do afterwards
- Explain that the intersection of two lines represents values satisfying both equations
- Find the approximate solution to a pair of simultaneous equations by reading a graph
- Verify a proposed solution by substituting into both equations
The lesson
Sometimes you have two equations at once, like y = x + 2 and y = 3x - 4. Solving them simultaneously means finding the one pair of x and y values that makes both equations true at the same time.
If you plot both equations as lines on the same graph, each line shows every point that fits its own equation. The two lines cross at one point. That crossing point is the only pair of values that satisfies both equations together.
Zara graphs y = x + 1 and y = -x + 5 on the same axes. The lines cross at the point (2, 3). She checks: for the first equation, 3 = 2 + 1 is true. For the second, 3 = -2 + 5 is true. So x = 2, y = 3 solves both equations.
To check a solution, put both values into both equations. If either equation comes out false, the point is wrong, or the graph was read a little off.
The crossing point of two lines is the one pair of values that makes both equations true.
Watch it
Where it sits
This opens up
Nothing builds on it yet.
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.