We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

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

7 Online Users