6.3 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

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

What is the first step in solving the system: y = 3x + 14 and y = -4x?

Back

Set the two equations equal to each other: 3x + 14 = -4x.

Front

What is the solution to the system: y = 3x + 14 and y = -4x?

Back

(-2, 8)

Front

What is the solution to the system: y = 5x and 3x + y = 24?

Back

(3, 15)

Front

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

Back

It means the lines represented by the equations are parallel and never intersect.

Front

What is the solution to the system: y = 3x and 12x - 4y = 20?

Back

No solutions.

Front

What is the first step in solving the system: x = 7 - 2y and 2x + y = 5?

Back

Substitute x in the second equation: 2(7 - 2y) + y = 5.

Front

What is the solution to the system: x = 7 - 2y and 2x + y = 5?

Back

(1, 3)