Jan 12 Solving Systems of Equations 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 if a system of equations has infinite solutions?

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

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

Back

The equations represent parallel lines that never intersect.

Front

How do you solve a system of equations by substitution?

Back

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

Front

What is the first step in solving the system of equations: y = 2x + 3 and 4x - y = 1?

Back

Substitute y from the first equation into the second equation.

Front

What is the solution to the system of equations: 2x + 3y = 6 and x - y = 1?

Back

(3, 0) is the solution.

Front

What does the term 'consistent' mean in relation to systems of equations?

Back

A consistent system has at least one solution.

Front

What does the term 'inconsistent' mean in relation to systems of equations?

Back

An inconsistent system has no solutions.

Front

What is the graphical representation of a system of equations with one solution?

Back

Two lines that intersect at a single point.

Front

What is the graphical representation of a system of equations with infinite solutions?

Back

Two overlapping lines.