How do I solve simultaneous equations?
The elimination method
2x + 3y = 83x + 2y = 7
First we multiply one or both of the equations so that one of their like terms share the same coefficients.
2x + 3y = 8 (multiply by 3) -> 6x + 9y = 243x + 2y = 7 (multiply by 2) -> 6x + 4y = 14
Now we can subtract the bottom equation from the top
5y = 10y=2
we then input this value into a previous formula2x + 3y = 82x = 8 - 3(2)2x = 2
x = 1
Alternatively
For questions where the elimination method does not leave one variable, such as:
x2 + y2 = 25y - 3x = 13
You should rearrange one of the equations in terms of one of its variables and then apply functions to it, such that it looks similar to the same term in the other equation.
y = 13 + 3x -> y2 = 9x2 + 78x + 169
Then you should substitute this equation into the other.
x2 + (9x2 + 78x + 169) = 25
Then simplify, and use the value found to find any other values, by inputting it into the original equations.
10x2 + 78x + 144 = 0 --> 5x2 + 39x + 72 = 0(5x + )(x + ) = 0 --> (5x + 24)(x + 3) = 05x + 24 = 0 x + 3 = 0x = -24/5 = -4.8 x = -3y = 13 +3x = 13 + 3(-3) = 13 - 9 = 4
y = 13 + 3x = 13 + 3(-24/5) = 65/5 - 72/5 = -7/5
x = -4.8, -3 y = 4, -7.5
