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 that are solved together.

Front

What does it mean for a system of equations to have infinite solutions?

Back

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

Front

What does it mean for a system of equations to have no solution?

Back

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

Front

What is the substitution method for solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into both equations; if both equations are true, the point is a solution.

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 variable.

Front

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

Back

Set 2x + 3 = -x + 1 and solve for x, then substitute back to find y.

Front

What is the graphical representation of a system of equations?

Back

The graphs of the equations plotted on the same coordinate plane.

Front

What does it mean if two lines intersect at a single point?

Back

The system of equations has one unique solution, which is the coordinates of the intersection point.

Front

How can you check your solution after solving a system of equations?

Back

Substitute the solution back into the original equations to verify that both equations are satisfied.