Solve 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 means to solve one equation for one variable and then substitute 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 5x + 4y = -14 and y = -7x - 15, what is the value of y when x = -2?

Back

y = -7(-2) - 15 = 14 - 15 = -1.

Front

What is the solution to the system 5x + 4y = -14 and y = -7x - 15?

Back

The solution is (-2, -1).

Front

What is the substitution method used for?

Back

To find the values of variables that satisfy all equations in a system.

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

Back

It means the equations represent the same line, so every point on the line is a solution.

Front

Given the equations x + 2y = 2 and x = -4y + 2, what is the value of y when x = 2?

Back

y = 0.

Front

What is the solution to the system x + 2y = 2 and x = -4y + 2?

Back

The solution is (2, 0).