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Solving Systems of Linear Equations using Substitution

Solving Systems of Linear Equations using Substitution 1.5 - Solution

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a

Let be the measure of the smaller angle and the measure of the greater angle. If the sum of these angles is we can write the first equation. We also know that the measure of the smaller angle, is less than the measure of the greater angle, This can be shown with an equation. Combining these equations we have the following system of equations.

b

To find the measure of the angles we need to solve the system for and When solving a system of equations using substitution, there are three steps.

  1. Isolate a variable in one of the equations.
  2. Substitute the expression for that variable into the other equation and solve.
  3. Substitute this solution into one of the equations and solve for the value of the other variable.
Since is already isolated in Equation (II), we can substitute into Equation (I) and solve the resulting equation for
Now, let's substitute into Equation (II) to find
We have found the measure of both angles. The measure of the greater angle is and the measure of the lesser angle is