Solving Linear Equations with Rock Icons
Hello everyone!! My honors Algebra II class had to make websites to help teach other students how to solve linear equations. Because I love punk rock music, I decided to theme my site accordingly. There are three methods to solving linear equations and I will show you all three on my site. I hope this site helps you...thanks for dropping by.
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Substitution Method |
| 3x + 4y = -4 x + 2y = 2 |
original equations |
| X + 2y = 2 -2y -2y x = -2y + 2 |
step 1 Subtract 2y from both sides of the equation to solve for x. The x= equation that remains will be substituted into the next equation. |
| 3x + 4y = -4 3 (-2y + 2) + 4y = -4 -6y + 6 + 4y = -4 -2y + 6 = -4 (-2y = -10) / -2 y = 5 |
step 2 Substitute the revised equation from step 1 into the second equation. Distribute the 3. Combine the like terms. Subtract the 6 from both sides of the equation and divide the equation by the coefficient of the y (-2). |
| X = -2y + 2 X = -2 (5) + 2 X = -8 (-8,5) |
step 3 Substitute the value found in step 2 into the revised equation from step 1. Solve. Final answer in coordinate form. |
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Linear Combination Method This method uses multiplication and addition to eliminate variables. An important thing to remember when using this method is that you may solve for any variable you choose first, but be sure when recording your answer that you put it in (x,y) form. |
Original Equations: |
x - 2y = -9 x + 3y = 16 |
Multiply the second equation by -1 to eliminate the x variables. Then combine like terms and divide to find the value of y. |
X
– 2y = -9 |
Go back to the original equations
and this time solve for x. |
3x - 6y = -27 |
Answer: |
(1,5) |
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Simply graph the equations you are
given and determine the answer by finding the one point
where the lines intersect. There are three possible
results. 1. One point where all equations intersect. 2.
Parallel lines, which means there are NO solutions. 3.
One equation (the equations are the same) which means
there are infinite answers. There are 2 methods for solving a
system of equations with graphing. One is to construct a
T-chart and the other is to just graph the equations on a
coordinate plane. |
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y = (2/3)x + 2/3 y = -4x + 24 |
ORIGINAL EQUATIONS |
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Construct a "T-chart" placing a column for the "x" values you will make up, a column for the first equation and another for the second equation. Look for the area where the 2 equations are equal. In this example that would be where y= 4. Therefor the answer is (5,4). |
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If the equations are not in y=
form, put them there. Then simply graph the lines |
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