Definition: A linear equation is an equation in which the highest power of the variable is 1. The general form is ax + b = c, where a, b, and c are constants.
Example 1: Solve for x in 5x − 3 = 12.
Step-by-Step Solution:
x:5x = 15x = 3Explanation: Each step isolates x by performing the inverse of the operations around it, making it simpler to find x’s value.
Example 2: Solve 7 − 2x = 3x + 1.
Solution Steps:
x to one side and constants to the other:6 = 5xx:x = 6/5Explanation: Rearranging terms simplifies the equation, isolating x for a clear solution.
Try these exercises:
x in 4x + 2 = 14x in 3x - 5 = 2x + 7Answers are provided below, but try to solve on your own first!
A system of linear equations consists of two or more linear equations that share the same variables. Solving the system means finding values for the variables that satisfy all equations simultaneously.
Example: Solve the system:
2x + y = 73x − y = 5
Solution using Elimination:
y:5x = 12 ⟹ x = 12/5x = 12/5 back into the first equation to solve for y:y = 11/5Solution: x = 12/5, y = 11/5.
Solve the system of equations:
x + y = 102x - y = 3
Choose the correct answer:
Definition: A linear equation is an equation in which the highest power of the variable is 1. The general form is ax + b = c, where a, b, and c are constants.
Solve the following equation:
Enter a linear equation in the form y = mx + b:
Solve equations in the form ax + b = c.
Identify the slope and intercept from equations like y = mx + b.
Solve equations in the form ax + b = c.
Identify the slope and intercept from equations like y = mx + b, and view the graph.