Aututmn's webpage 
Hi my name is Autumn.  I go to school at Union Grove High School.  I am creating this website to show you how to do the substution method, linear equations, and word problems!  Have fun!
 
y=5-4x
3x-2y=12

3x-2(5-4x)=12
3x-10+8x=12
11x-10=12
(add 10 to both sides)
11x=22
(divided both by 11)
x=2

y=5-4(2)
y=5-8
y=-3
  • Steps for using Linear Equations:
  • write both equations in the form Ax+By=C
  • clear any decimals or fractions
  • chose a variable to eliminate
  • make the chosen variables term additives inverse by multiplying one or both equations by a number.
  • Eliminate the variable by adding the equations
  • substitute to solve for the remaining variable
3x-4y=-15
3x-4(-5x-2)=-15
3x+20x+8=-15
23x+8=-15
(minus 8 on both sides)
23x=-23
(divided by23 on both sides)
X=1

5x+y=-2
-5x       -5x
y=-5x-2
y=5(-1)-2
y=5-2
Y=3
  • solving using the substitution method
  • solve one of the equations for Y
  • Substitute that equation into the Y in the second equation
  • it then gives one big equation with one variable so you can solve for it
  • then substitute that answer into the remaining variable from the first problem 
  • solve it, then you have your x and y
x+y=180
x+8+3x=180 
4x+8=180
-8    -8
4x=172
(divided both by 4)
x=43

y=8+3x
y=8+3(43)
y=8+129
y=137
  WORD PROBLEM: The measure of one of two supplementary angles is 8 degrees more than three times the other.  Find the measure of the larger of the two angles.
Two Supplementary angles equal 180.  Then I substituted the 8 and the 3 times into the problem and solved for x and y.

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