Solving Systems: 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 means to solve one equation for one variable and then substitute that expression into the other equation.

Front

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

Back

y = 3.

Front

What is the first step in solving the system: y = 4x - 1 and y = 2x + 1?

Back

Set the two equations equal to each other: 4x - 1 = 2x + 1.

Front

What is the solution to the system: y = x - 2 and -2x + 3y = -1?

Back

(5, 3).

Front

How do you isolate a variable in an equation?

Back

You perform operations to get the variable on one side of the equation by itself.

Front

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

Back

(-2, -1).

Front

What does it mean if two lines intersect at a point?

Back

It means that the system of equations has one unique solution.

Front

What is the graphical representation of a system of equations?

Back

It is the point(s) where the lines representing the equations intersect.

Front

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

Back

(1, 3).