Solving Systems by Substitution

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is substitution in the context of solving equations?

Back

Replacing one variable with an expression derived from another equation.

Front

How do you use substitution to solve a system of equations?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

What is the first step in solving the system: y = 8 and y = -4x + 4?

Back

Substitute y = 8 into the second equation: 8 = -4x + 4.

Front

What is the solution to the system: y = 3x - 8 and y = 4 - x?

Back

(3, 1) is the solution.

Front

What does it mean if a system of equations has one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

What does it mean if a system of equations has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinite solutions?

Back

The lines representing the equations coincide, meaning they are the same line.

Front

Solve the system: y = -1x - 5 and 4x - 8y = 4.

Back

The solution is (-3, -2).