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Another approach to solving a problem is dividing the task into appropriate sub-goals. As you reach each sub-goal, you take another step toward solving the original problem. Consider this system of equations:

2x + y – 3z = 1

x + 2y + 5z = 9

3x – 3y – 10z = 4

Use sub-goals to solve for the variables x, y, and z.


1. The first sub-goal is to derive a system of 2 equations in two variables from the system of 3 equations. Eliminate x by doubling the second equation and subtracting the first equation from this doubled equation. 


2. Obtain another 2-variable equation in y and z by multiplying the second equation by 3 and subtracting the third equation from it. 


3. The second sub-goal is to solve for z. Hint: You can multiply the first equation in y and z by -3. Then add the result to the second equation in y and z.


4. The final sub-goal is solve for x and y. Place the answer in this format, (x, y, z). Hint : Substitute the value of z you obtained into one of the 2-variable equations and obtain y. Then substitute the values of z and y into one of the 3-variable equations to obtain the value of x.


5. Apply sub-goals to find the percentage of perfect squares between 1 and 100, inclusive, that are odd. Round to the nearest percentage if necessary. Hint: Consider five sub-goals. 1) List all perfect squares from 1 to 100. 2) Count the number of odd squares. 3) Divide the number of odd squares by the total number of squares. 4) Convert the fraction to a percentage. 5) If needed, round your answer to the nearest percentage.


They didn't teach me how to do this, please help.

 Mar 29, 2019

Sorry, that's a lot. I can probably make do with just help on the first two. 

 Mar 29, 2019

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