Example 1. Solve simultaneously for x and y.
| 2x | + | y | = | 4 |
| x | − | y | = | −1 |
Solution. In this case, the solution is not obvious. Here is a general strategy for solving simultaneous equations:
When one pair of coefficients are negatives of one another,
add the equations vertically, and that unknown will cancel.
We will then have one equation in one unknown, which we can solve.
add the equations vertically, and that unknown will cancel.
We will then have one equation in one unknown, which we can solve.
Upon adding those equations, the y's cancel:
| 2x | + | y | = | 4 |
| x | − | y | = | −1 |
| __________________________________ | ||||
| 3x | = | 3 | ||
| x | = | 3 3 |
||
| x | = | 1. | ||
To solve for y, the other unknown :
Substitute the value of x in one of the original equations.
Upon substituting x = 1 in the top equation:
| 2· 1 + y | = | 4 |
| y | = | 4 − 2 |
| y | = | 2. |
If we report the solution as an ordered pair, then the
solution is (1, 2) i.e. x = 1 & y = 2. Those are the coordinates of the point of
intersection of the two lines.
This method of solving simultaneous equations is called the method of elimination.
Time for a quiz to check your understanding:
In pairs, answer the questions in the quiz .
