Substitution Method

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables that are solved together.

Front

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

Back

It means there are unlimited pairs of (x, y) values that satisfy both equations.

Front

Solve the system of equations by substitution: y = -4x + 5 and y = 3x - 16.

Back

(3, -7)

Front

Solve for (x, y) given: x = y - 2 and 4x + y = 2.

Back

(0, 2)

Front

Solve the system: x = -3y - 17 and 2x + 3y = -7.

Back

(10, -9)

Front

What is the first step in the substitution method?

Back

Isolate one variable in one of the equations.

Front

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

Back

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

Front

What is the graphical representation of a system of equations with no solution?

Back

Two parallel lines that never intersect.

Front

What is the graphical representation of a system of equations with infinite solutions?

Back

Two lines that overlap completely.

Front

What is the substitution method used for?

Back

To solve systems of equations by replacing one variable with an expression from another equation.