Solve Systems by Substitution

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation to find the values of both variables.

Front

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

Back

A system has no solution if the equations represent parallel lines that never intersect.

Front

How do you determine if a system of equations has one solution?

Back

A system has one solution if the equations represent lines that intersect at exactly one point.

Front

What is the first step in solving a system of equations by substitution?

Back

The first step is to solve one of the equations for one variable in terms of the other variable.

Front

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

Back

(-3, -9)

Front

What is the solution to the system y = -2x + 18 and y = 8?

Back

(5, 8)

Front

How do you check the solution of a system of equations?

Back

Substitute the solution back into both original equations to verify that both equations are satisfied.

Front

What does it mean if two equations in a system are equivalent?

Back

If two equations are equivalent, they represent the same line and thus have an infinite number of solutions.

Front

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

Back

(-8, 35)

Front

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

Back

The point of intersection represents the solution to the system, indicating the values of the variables that satisfy both equations.