Linear Equations & Solving 2x2 Linear Systems

Math 1310
Section 2.1: Linear Equations

Definition: To solve an equation in the variable x using the algebraic method is to use the rules of algebra
to isolate the unknown x on one side of the equation.

Definition: To solve an equation in the variable x using the graphical method is to move all terms to one
side of the equation and set those terms equal to y. Sketch the graph to find the values of x where
y = 0.

Example 1: Solve the fol lowing equation algebraically.

5 + 6 = −18 − y

Example 2: Solve following equation algebraically.

7 + 2(3 – 8x) = 4 – 6(1 + 5x)

Example 3: Solve following equation algebraically.

Example 4: Solve following equation algebraically.

Example 5: Find the x- intercept and y -intercept of the following equation. Express the answers in
coordinate point form.

a. −7x + 8y − 63 = 0

b. x²− y − 16 = 0

c. 4x² − y² − 81 = 0

Math 1310
Section 6.1: Solving 2x2 Linear Systems

To solve a system of two linear equations

means to find values for x and y that satisfy both equations.
The system will have exactly one solution , no solution, or infinitely many solutions.

1. Exactly one solution, will look like :

2. No solution, will look like:

3. Infinitely many solutions, will look like:

Example 1: Solve the following systems of linear equations by the substitution method .

Example 2 : Solve the following systems of linear equations by the substitution method

Example 3: Solve the following systems by the Elimination Method .

Example 4: Solve the following systems by the Elimination Method.