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 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

If y = 2x + 1, what is y when x = 3?

Back

y = 2(3) + 1 = 7.

Front

What is the solution to the system: y = -2x + 5 and y = 2x - 11?

Back

(4, -3).

Front

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

Back

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

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

Solve the system: y = 4x - 1 and -2x + y = 1. What is the solution?

Back

(1, 3).

Front

What is the substitution method used for?

Back

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