Solving Systems of Equations by Substituting or Eliminating

Compare and contrast the substitution and elimination methods for solving a system of equations.

• Substitution method always leads to the correct solution, while elimination method is unreliable

• Substitution method involves adding the equations together, while elimination method involves multiplying the equations

• Both methods involve manipulating the equations to solve for one variable and then substituting or eliminating that variable to solve for the other variables.

• Substitution method only works for linear equations, while elimination method only works for quadratic equations

When solving the system, if you get a result of something like 6 = 6 or -2 = -2 and the answer is:

• No Solution

• Infinitely Many Solutions

• Not possible

• (6,-2)

a method used to solve a system of equations which involves solving the equations for one variable and then substituting that expression into the other equation

• graphing

• evaluate

• elimination

• substitution

What is another term for systems of equations?

• Simultaneous Equations

• Linear Functions

• Linear Equations

• y-intercept

What is a solution in a system of equations?

• The set of values that makes all of the equations in the system true

• A system of equations that has no set of values which will satisfy both equations

• A system of equations that has one intersection

• A system of equations in which both equations are exactly the same

a method used to solve a system of equations which involves eliminating one of the variables by adding or subtracting the equations

• elimination

• evaluate

• substitution

• graphing

a situation where there is one or infinitely many solutions that satisfies all of the equations in the system; this happens when lines are intersecting

• no solution

• consistent system

• inconsistent system

• parallel lines

Solve for x and y
3x + 2y = 16
7x + y = 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

y = -6x + 5
-2x + y = 5

• (-3, -6)

• (-6, 3)

• (0, 5)

• (-3, 5)

6x + y = -1
y = -3x - 4

• (3, 1)

• (1, 7)

• (-3, 1)

• (1, -7)