Solving systems by substitution

A system of two linear equations, such as 2x + 3y = 31 and 5x -y = 1 is usually solved by elimination or substitution. (Refer to Algebra For Dummies if you want a full explanation of each type of solution method.) For the problems in this chapter, I use the substitution method, to solve for a variable. This means that you change the format of one of the equations so that it expresses what one of the variables is equal to in terms of the other, and then you substitute into the other equation. For example, you solve for y in terms of x in the equation 3x + y = 11 if you subtract 3x from each side and write the equation as y = 11 - 3x. 

Consider solving the system 2x + 3y = 31 and 5x-y = 1. First go to the second equation and rewrite it with y on one side and everything else on the other side. You choose the second equation, because the y variable has a coefficient of -1. Having a coefficient of 1 or -1 is desirable, because you can avoid working with fractions. 

To solve for y in terms of x in 5x -y = 1, you first add y to each side of the equation and then subtract 1 from each side. 

Now substitute into the first equation. Because y = 5x - 1, replace the y in the first equation with 5x - 1 and solve for x. 

The rest of this chapter deals with how to use substitution in systems of equations to solve word problems. 

---