Solve systems of linear equations with elimination (advanced)

The  exercise appears under the Algebra I Math Mission. This exercise practices solving systems of equation with multi-step elimination (e.g., a manipulation is need in order for x-values or y-values to cancel each other out).

Types of Problems
There is one type of problem in this exercise:


 * 1) Solve the following system of equations.: This problem presents two equations with the $$x$$ and $$y$$ equations for elimination. The student is expected to use elimination and solve the system of the equation. The answer is to be typed in the text boxes below as an x and a y-coordinate. Solve systems of linear equations with elimination (basic).PNG

Strategies
Knowledge of the elimination method of solving equations will help to perform this exercise accurately and efficiently.
 * 1) Students can replace one of the equations with the sum of the two equations and obtain an equivalent system that has the same solution.
 * If, by doing that, they obtain an equation with a single variable, we will be able to find the solution for that variable. This is called the elimination method.
 * 1) We can see that the coefficients of the variable $$x$$ have opposite signs in the two equations. By adding the equations, we can eliminate $$x$$ as follows.

Real-life applications

 * 1) Applications include supply and demand lines form business and various other situations where there is information gained from different resources.