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 to solve a system of equations?

Back

Finding the values of the variables that make all equations true at the same time.

Front

What is substitution 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

How do you isolate a variable in an equation?

Back

Rearranging the equation to get the variable on one side and the constants on the other.

Front

What is the first step in solving the system: y = 3x - 5 and 2x + 4y = -6?

Back

Substitute y from the first equation into the second equation.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

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

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines representing the equations.

Front

How can you check if your solution to a system is correct?

Back

Substitute the solution back into the original equations to see if they hold true.

Front

What is the solution to the system: y = 3x - 5 and 2x + 4y = -6?

Back

(1, -2)