Solving Systems by 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 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 + 3, what is y when x = 4?

Back

y = 2(4) + 3 = 11.

Front

What is the solution to the system of equations: y = 3x - 8 and y = 4 - x?

Back

(3, 1)

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 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 a unique solution at that point.

Front

What is the solution to the system: y = 5x + 1 and y = 3x + 13?

Back

(6, 31)

Front

What is the graphical representation of a system of equations?

Back

It is the intersection point(s) of the lines represented by the equations.