Precalculus : Solve Systems of Linear Equations

Study concepts, example questions & explanations for Precalculus

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Example Questions

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Example Question #11 : Inequalities And Linear Programming

Find the point of intersection by using Gaussian elimination:

Possible Answers:

Correct answer:

Explanation:

To solve this, let's first try to eliminate x. We can do this by adding the two equations:

     

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Which implies

 

We can now solve for x by plugging 2 in for y in either equation.

Thus we have the answer 

 

Example Question #11 : Inequalities And Linear Programming

Solve the following system of equations:

Possible Answers:

Correct answer:

Explanation:

Let's solve this equation by eliminating the variable x by adding a multiple of the second equation to the first.

        

  

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Now let's combine those y values and solve for y.

Now all we have to do is plug that in for y in either original equation to solve for x.

 

Thus this yields the intersection point 

 

Example Question #11 : Solve Systems Of Linear Equations

Solve the following system of equations for the intersection point in space:

Possible Answers:

Correct answer:

Explanation:

Because one of the variables, z, has already been isolated, let's use the substitution method to solve this system of equations. We know z = 1, so let's plug that into the middle equation to solve for y:

Now that we have found y, let's solve for x by plugging both y and z into the top equation:

Thus we have found that the point of intersection would be

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