Solving linear equations with two variables | ||||||||||||||
In the last posting titled "Basic Linear equations", we covered the basics of solving an equation with one "unknown". There are rules that govern linear equations that we did not cover in the last posting. I will be covering those rules here before we move on to linear equations with two unknowns. Rules that govern linear equationsRule 1: unknown variables can not be multiplied by itself or another variable. unknown variables shall not be devided by one another in linear equation. For example, the equations xy=4 and x*x = 10 violates the linear equation rule. why? Consider this: If we were to solve for x in xy = 4, to solve this equation, we are reqyured to isolate one variable and solve the equation in terms of the other variable. In our case we can not isolate x or y without deviding by the one or the other, which is against the rule of linear equations. Rule number 3: For an equation to be linear, such an equation shall not have a variable under the root sign. Solving a linear equationNow that we have laid out the rules, let us solve our first linear equation with two variable:
To test the equation we substitute (x by 5 - y in the original equation): => 4 * (5-y) + 4y = 20 => 4 * 5 => 20 = 20 Since the substituting our anser into the equation produces results that balances the left and right sides of our equation, we can be sure the answer our answer (x = 5 - y) is correct. |
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