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Solving Systems of Linear Equations using Substitution

Solving Systems of Linear Equations using Substitution 1.2 - Solution

arrow_back Return to Solving Systems of Linear Equations using Substitution
a

When solving a system of equations using substitution, there are three steps.

  1. Isolate a variable in one of the equations.
  2. Substitute the expression for that variable into the other equation and solve.
  3. Substitute this solution into one of the equations and solve for the value of the other variable.
Here we want to solve the following system. Observing the given equations, it looks like it will be simplest to isolate in Equation (I). Next we will substitute for in Equation (II) and solve the resulting equation for
Now, to find the value of we need to substitute into either of the equations. Let's substitute it into Equation (I).
The solution, or point of intersection, to this system of equations is the point
b
Here we have been asked to solve the following system of equations. When solving a system of equations using substitution we first want to isolate one variable in one of the equations. Let's isolate in Equation (II). Next we will substitute for in Equation (I). After that we will solve the resulting equation for
Now that we know that we can substitute this in any of the equations. Let's substitute it into We then get an equation we can solve for
Solve for
The solution, or point of intersection, to this system of equations is the point
c
We are now going to solve the system using the substitution method. As a first step we will isolate the variable in Equation (I).
Let's in Equation (II) substitute for and solve the resulting equation for
To find we will substitute into Equation (II).
Solve for
The solution, or point of intersection, to this system of equations is the point