Week 12- Solving Systems Algebraically

This week we learned how to solve systems algebraically with more than one variable.

For example: x+6y=4 and 0=x-4y

In these types of systems you used steps.

  1. Isolate a variable
  2. Plug the equation for that variable into the second system
  3. solve for that variable
  4. plug variable into original equation, solve for the missing variable
  5. Check!

This may not make complete sense in steps, so I’ll demonstrate using the first example.

  1. x+6y=4 can be rearranged to make x=4-6y
  2. next you plus your new equation x=4-6y into your second equation: 0=x-4y which turns into 0=(4-6y)-4y. This becomes y=2/5.
  3. Next, we plug our value for y into our original first equation x+6y=4, which becomes x+6(2/5)=4
  4. Simplifying the equation: x=1.6
  5. Check y=2/5 and x=1.6: x+6y=4 -> 1.6+6(2/5)=4 Yes! 0=x-4y -> 0=1.6-4(2/5) Yes! So we know we did it correctly

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