Solving Systems by 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 to solve a system of equations by graphing?

Back

It means to plot the equations on a graph and find the point(s) where they intersect.

Front

What is substitution in the context of solving systems of equations?

Back

Substitution is a method where you solve one equation for one variable and then substitute that expression into the other equation.

Front

What is the solution of a system of equations?

Back

The solution is the point(s) 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 representing the equations are parallel and never intersect.

Front

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

Back

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

Front

How do you determine if a system of equations has one solution?

Back

If the lines intersect at exactly one point, the system has one solution.

Front

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

Back

Isolate one variable in one of the equations.

Front

If you have the equations y = 2x + 3 and y = -x + 1, how do you solve by substitution?

Back

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

Front

What is the graphical representation of the solution (3, 4)?

Back

It is the point where the lines of the equations intersect at x=3 and y=4.