Adapted from Walch Education Proving Equivalencies
Slide 3
Two equations that are solved together are called systems of
equations. The solution to a system of equations is the point or
points that make both equations true. Systems of equations can have
one solution, no solutions, or an infinite number of solutions.
Solutions to systems are written as an ordered pair, (x, y).
Systems of Equations
Slide 4
Solve one of the equations for one of the variables in terms of
the other variable. Substitute, or replace the resulting expression
into the other equation. Solve the equation for the second
variable. Substitute the found value into either of the original
equations to find the value of the other variable. Solving Systems
of Equations by Substitution
Slide 5
Multiply each term of the equation by the same number. It may
be necessary to multiply the second equation by a different number
in order to have one set of variables that are opposites or the
same. Add or subtract the two equations to eliminate one of the
variables. Solve the equation for the second variable. Substitute
the found value into either of the original equations to find the
value of the other variable. Solving Systems of Equations by
Elimination Using Multiplication
Slide 6
Solve the following system by elimination. Practice # 1
Slide 7
Add the two equations if the coefficients of one of the
variables are opposites of each other. 3y and 3y are opposites:
Simplify : 3x = 0 Solve the equation for the second variable. x = 0
We are half way there!!!
Slide 8
Substitute the found value, x = 0, into either of the original
equations to find the value of the other variable. 2x 3y = 11First
equation of the system 2(0) 3y = 11Substitute 0 for x. 3y =
11Simplify. Divide both sides by 3. If graphed, the lines would
cross at
Slide 9
Dont worry, we will practice elimination method and
substitution method in class!