Solving Systems 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

If y = 2x + 3, what is y when x = 2?

Back

y = 2(2) + 3 = 7.

Front

What does it mean if two lines are parallel in a system of equations?

Back

It means there is no solution because the lines never intersect.

Front

What is the solution to the system: y = 3x + 1 and y = -x + 5?

Back

(1, 4) is the solution.

Front

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

Back

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

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

Back

It means the equations represent the same line.

Front

What is the substitution method?

Back

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