Solving Systems of Equations by Substitution and Elimination

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 two equations to intersect on a graph?

Back

It means that the solution (x, y) is the point where both equations are true.

Front

What is the substitution method in 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

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

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

Back

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

Front

How do you determine if a system of equations has no solution?

Back

If the equations represent parallel lines, they will never intersect, indicating no solution.

Front

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

Back

Get both equations in standard form and line up the like terms.

Front

How do you convert an equation to slope-intercept form?

Back

Rearrange the equation to the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the standard form of a linear equation?

Back

Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

What is the purpose of lining up like terms in elimination?

Back

To easily add or subtract the equations to eliminate one variable.