5.3 Solving Systems by Substitution

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 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 an infinite solution in a system of equations?

Back

It occurs when the equations represent the same line, resulting in countless solutions.

Front

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

Back

It means the equations represent parallel lines that never intersect.

Front

How do you isolate a variable in an equation?

Back

By performing inverse operations to get the variable alone on one side of the equation.

Front

Solve the system by substitution: y = -2x - 5 and -x - 4y = -15.

Back

(-5, 5)

Front

Solve the system by substitution: 2x - 5y = 12 and y = -4.

Back

(-4, -4)

Front

Solve the system by substitution: 4x + 2y = 6 and y = 3x - 17.

Back

(4, -5)

Front

Solve the system by substitution: 5x + 2y = 19 and y = 2.

Back

(3, 2)

Front

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

Back

Choose one equation and solve for one variable in terms of the other.