Solving Systems of Equations by Substitution
To solve a linear system of equations by the method of substitution:
1) first solve for one of the variables in one of the
equations … it does not matter if you solve for x or y … check both
equations and solve for the variable that has the smallest coefficient,
Solve the system of equations … 3x – 2y = 19 and x + y = 8 … by substitution.
First, exam both of the equations and decide for which variable to solve. Since the second equation has both an x term and a y term with coefficients of 1, I can choose to solve for either x or y in the second equation. I choose to solve for x in the second equation. Solving for x, I find that x = 8 – y. Now, I use the value for x, which is 8 – y, and substitute that value into the first equation for the value of x.
3(8 – y) – 2y = 19 … now solve for y
24 – 3y – 2y = 19
– 5y = 19 – 24
– 5y = – 5
y = 1 … now use this value and
substitute it into either of the original equation to find the value of x.
3x – 2(1) = 19
3x = 19 + 2
3x = 21
x = 7 … the solution set is the point ( 7, 1 )
Check: the solution set should work in both of the
equations 3x – 2y = 19 and x + y = 8.
The views and
opinions expressed in this page are strictly those of Mary Lou Baker. This page was
This page was edited on 19-Sep-2007