Solving Systems with 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 no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

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

Back

It means that the equations represent the same line, so every point on the line is a solution.

Front

How do you solve a system of equations using substitution?

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 of equations: y = 2x + 3 and x + y = 10?

Back

Substitute the expression for y from the first equation into the second equation.

Front

If you have the equations y = 3x + 1 and y = -x + 5, how do you find the solution?

Back

Set 3x + 1 equal to -x + 5 and solve for x.

Front

What is the solution to the system of equations: 2x + 3y = 12 and y = 2x - 1?

Back

(3, 2) is the solution.

Front

What does it mean if two equations in a system are identical?

Back

It means they represent the same line and have infinite solutions.

Front

How can you tell if a system of equations has no solution by looking at the graphs?

Back

If the lines are parallel, the system has no solution.

Front

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

Back

The two lines overlap completely on the graph.