Solve 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 simultaneously.

Front

What does it mean to solve a system by substitution?

Back

To solve a system of equations by expressing one variable in terms of the other and substituting 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 y = -2x + 18 and y = 8, what is the solution?

Back

(5, 8)

Front

Given the equations y = -2x + 5 and y = 2x - 11, what is the solution?

Back

(4, -3)

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 do not intersect.

Front

Given the equations y = 4x + 3 and 2x - 3y = 21, what is the solution?

Back

(-3, -9)

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines representing the equations.

Front

What is the significance of the point of intersection in a system of equations?

Back

It represents the solution to the system, where both equations are satisfied.

Front

Given the equations y = -3x + 11 and y = -6x - 13, what is the solution?

Back

(-8, 35)