Topic 4.2 Solving Systems by Substitution

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean to solve a system of equations by substitution?

Back

It means to solve one equation for one variable and then substitute that expression into the other equation.

Front

What is the solution to a system of equations?

Back

The point (x, y) where the equations intersect, representing the values of the variables that satisfy all equations.

Front

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

Back

It means the lines represented by the equations are parallel and never intersect.

Front

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

Back

It means the equations represent the same line, and there are countless points of intersection.

Front

How do you determine if a system of equations has no solution?

Back

If, after simplification, you get a false statement like 4 = 7.

Front

How do you determine if a system of equations has infinite solutions?

Back

If, after simplification, you get a true statement like 2 = 2.

Front

What is the first step in solving a system of equations by substitution?

Back

Solve one of the equations for one variable in terms of the other.

Front

Given the equations y = 2x + 3 and y = -x + 1, how do you solve for x?

Back

Set 2x + 3 = -x + 1 and solve for x.

Front

What is the solution to the system: x - y = 6 and y = 2x - 5?

Back

(-1, -7).