Systems of Equations- Graphing & 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 for two lines to intersect on a graph?

Back

It means they have a common solution, which is the point where they meet.

Front

What is the graphical representation of a solution to a system of equations?

Back

The point where the lines representing the equations cross.

Front

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

Back

The lines are parallel and never intersect.

Front

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

Back

The lines are the same, meaning they overlap completely.

Front

How do you solve a system of equations using substitution?

Back

You solve one equation for one variable and substitute that expression into the other equation.

Front

What is the first step in solving the system by substitution?

Back

Isolate one variable in one of the equations.

Front

If y = 2x + 3, what is y when x = 4?

Back

y = 2(4) + 3 = 11.

Front

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

Back

(1, 3) - the point where the two lines intersect.

Front

What does the term 'no solution' indicate in a system of equations?

Back

It indicates that the equations represent parallel lines.