Unit 2 lesson 8

Lesson 8: Solving Systems of Equations with Substitution Method

In this lesson, we will discuss how to solve systems of equations using the substitution method. The substitution method involves solving one of the equations for one variable and then substituting that expression into the other equation. This allows us to isolate and solve for the remaining variable.

Let's consider the following system of equations:

Equation 1: 2x + y = 5
Equation 2: 3x - 2y = 4

Step 1: Solve one of the equations for one variable. Let's solve Equation 1 for y:

y = 5 - 2x

Step 2: Substitute the expression (5 - 2x) for y in Equation 2.

3x - 2(5 - 2x) = 4
3x - 10 + 4x = 4
7x - 10 = 4
7x = 14
x = 2

Step 3: Substitute the value of x back into the expression for y in Equation 1.

2(2) + y = 5
4 + y = 5
y = 1

Therefore, the solution to the system of equations is x = 2 and y = 1.

By using the substitution method, we can efficiently solve systems of equations and find the values of the variables that satisfy both equations. Practice solving more systems of equations using the substitution method to improve your skills in solving linear equations.