Solving Systems of Equations

Many applications in real-life contain two or more unknowns. To solve such problems, we must write as many independent equations as there are unknowns. Otherwise, it is not possible to obtain numerical answers. This section mirrors what you’ve already been doing this unit – that is, solving systems with two or…

There are practically countless methods devised over the past millennia that have enabled mathematicians to solve systems with three unknowns. In this section, we will focus on one method exclusively which is based on the methods that you’ve already learned when you solved systems with two unknowns. Technically, when a…

In this section, you’ll use the method of addition-subtraction or the method of substitution to solve systems of equations with literal coefficients (coefficients that aren’t numbers). To do this, you treat the coefficients as if they were numbers, keeping in mind what you’ve learned in the past about combining like-terms.…

This lesson will explore how to use the techniques used in the previous method to solve non-linear equations. Specifically, we’ll look at a system of equations whose variable is found in the denominator. null Notice that both equations displayed above consist of terms whose variables (x and y) are positioned…

Elimination Method In the elimination method (also known as the addition-subtraction method), we eliminate one of the unknowns by first (if necessary) multiplying each equation by a factor will make the coefficients of one unknown in both equations equal, regardless of their signs. The two equations are then added or subtracted…

This chapter introduces us to solving a system of equations. In part one of this course (Math 1131), you learned how to solve linear equations (such as, 25 = x + 5), for the unknown variables. This time you’ll learn to solve a system of linear equations with two unknowns,…