Solve simultaneous equations graphically
If an equation has a single unknown, we can usually solve it
x + 5 = 15 x = 10
However if an equation has two unknowns, it is usually impossible to solve.
3x + 4y = 22
There are infinite combinations of x and y that could be substituted into this equation to give 22, and so there is no single solution for the value of x and y.
For example, substituting the following into the equation will all produce 22
x = 0, y = 5.5
x = 22/3, y = 0
x = 2, y = 4
If we are provided with a second equation, however, then there will be only a single solution (if both equations are linear)
3x + 4y = 22
-2x + 4y = 12
There is now only a single solution for x and y that will produce both 22 in the first equation, and 12 in the second: x = 2, y = 4.
To solve the simultaneous equations graphically is fantastically easy to solve
Plot the two equations See where they cross – the coordinates where the two graphs cross are the solutions for x and y
The graphs will cross only once if both are linear. If one of them is non-linear, then they may cross once, twice, or sometimes not at all.
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