Solving Linear Equations and Systems - basics

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form ax + b = c, where a, b, and c are constants.

Front

How do you solve a linear equation?

Back

To solve a linear equation, isolate the variable on one side of the equation using inverse operations (addition, subtraction, multiplication, division) until the variable is alone.

Front

What does it mean to solve a system of equations?

Back

Solving a system of equations means finding the values of the variables that satisfy all equations in the system simultaneously.

Front

What is substitution in solving systems of equations?

Back

Substitution is a method where you solve one equation for one variable and then substitute that expression into the other equation.

Front

What is the solution to the equation 7x - 3x - 8 = 24?

Back

x = 8.

Front

What is the solution to the equation 3(5x + 1) = 48?

Back

x = 3.

Front

What is the solution to the equation x/7 = 14?

Back

x = 98.

Front

How do you find the solution to the system of equations x = 6 and y = 2x - 3?

Back

Substituting x = 6 into y = 2(6) - 3 gives y = 9, so the solution is (6, 9).

Front

What is the solution to the system of equations y = 2x + 1 and y = 4x - 1?

Back

The solution is (1, 3).

Front

What is the graphical representation of a linear equation?

Back

The graphical representation of a linear equation is a straight line on a coordinate plane.