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?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is the substitution method?

Back

A method for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

What is the first step in solving a system using substitution?

Back

Get either variable by itself.

Front

If y = 3 - x, what is x when y = 1?

Back

x = 2.

Front

Solve for y: y = 4x - 10 when x = 5.

Back

y = 10.

Front

What is the solution to the system: y = 8x + 1 and y = 6x + 3?

Back

(1, 9).

Front

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

Back

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

Front

What is the graphical representation of a system of equations?

Back

The point(s) where the lines representing the equations intersect.

Front

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

Back

The lines are parallel and do not intersect.