Solving linear equations:
Follow these basic steps to solve linear equations:
- Aggregate the constant terms and variable terms
- For equations with more than one variable, eliminate variables by substituting equations in their place.
- Hence, for two equations with two variables x and y, express y in terms of x and substitute this in the other equation.
- For example, x+y=14 and x+4y=26 => x=14-y. Substituting this in equation 2, we get 14-y+4y=26. Hence y=4 and x=10.
For equations of the form ax+by=c and mx+ny=p, find the LCM of b and n. Multiply each equation with a constant to make the y term coefficient equal to the LCM. Then subtract equation 2 from equation 1.
Example:
Let 2x+3y=13 and 3x+4y=18 are the given equations (1) and (2).
- LCM of 3 and 4 is 12.
- Multiplying (1) by 4 and (2) by 3 we get 8x+12y=52 and 9x+12y=54.
- (2)-(1) gives x=2, y=3
