Solving Systems of Equations Algebraically Elimination

Preview Announcements Standards and Objectives Recap of Systems Systems with Similar Coefficients Systems with Different Coefficients Making a Plan Practice

Announcements Make sure you review how to solve systems Quiz Tomorrow on Graphing and Substitution If you want help, I’ll stay any day this week (except today) until 5pm. Quiz Wednesday on what we do today

Standards and Objectives SPI Solve systems of three linear equations in three variables. – Solve a three by three system of linear equations algebraically

Recap of Systems Solution is the point where the graphs of the equations would meet. You may have 1 solution, given as the point (x,y) You may have no solutions if the two lines never meet. You may have many solutions if the two lines are identical.

Ways to solve systems Solving them by graphing If you can write all equations in y= form Graph them Use the calculator to find the intersection Can easily end up with fractions Some equations aren’t easy to solve for y Solving them by substitution If you can solve one equation for a variable Don’t have to graph them You get a more precise answer Can end up with fractions Some equations aren’t easy to solve for a variable

Solving Systems Using Elimination Very useful if we can’t get equations into y= or x= form We don’t have to manipulate equations as much Will still give us a precise answer for fractions and decimals Don’t have to graph them

Some systems are kind of hard to solve Solving this for x or y gives us fractions If we tried this, we would still end up combining the two equations…

Now…we add another method: ELIMINATION We want to eliminate a variable…any suggestions? Add/Subtract the equations. Solve for remaining variable…

Plug in and done Plug in value into either equation. Solve for the other variable. Check your answer by plugging in x and y… are the equations both balanced?

Let’s try some more…

What if the coefficients don’t match? Make coefficients equal in value and opposite in sign by multiplying… Everything else goes the same way

Plug in and done Plug in value into either equation. Solve for the other variable. Check your answer by plugging in x and y… are the equations both balanced?

Let’s try some more…

Let’s make a plan… As a class, help me make up some problems that would work easily for: – Graphing – Substitution – Elimination

Use these examples to decide how you would approach solving systems of equations.

Practice… p.146, #’s 22-38, 53 Show your work. Remember, our goal is to get one variable to cancel. Pick the variable that you can cancel easiest.