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
The views and
opinions expressed in this page are strictly those of Mary Lou Baker.
This page was edited on 19-Sep-2007