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.

Front

What does it mean to solve a system of equations by substitution?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Front

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

Back

Isolate one variable in one of the equations.

Front

Given the equations y = -2x + 5 and y = 2x - 11, what is the solution?

Back

(4, -3)

Front

How do you check if a solution is correct for a system of equations?

Back

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

Front

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

Back

The lines represented by the equations are parallel and never intersect.

Front

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

Back

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

Front

Given the equations 2x + y = 5 and y = 2x - 11, what is the solution?

Back

(4, -3)

Front

What is the graphical representation of a system of equations?

Back

It is represented by the intersection points of the lines on a coordinate plane.

Front

What is the substitution method?

Back

A method for solving systems of equations by replacing one variable with an equivalent expression.