PSAT Math : How to find the solution for a system of equations

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #32 : Basic Arithmetic

What is the solution of  for the two systems of equations?

Possible Answers:

Correct answer:

Explanation:

We first add both systems of equations.

Left Hand Side:

Right Hand Side:

Our resulting equation is:

 

We divide both sides by 3.

Left Hand Side:

Right Hand Side:

Our resulting equation is:

Example Question #3 : Creating Equations With Whole Numbers

What is the solution of  for the two systems?

Possible Answers:

Correct answer:

Explanation:

We first multiply the second equation by 4.

So our resulting equation is:

Then we subtract the first equation from the second new equation.

Left Hand Side:

Right Hand Side:

Resulting Equation:

 

We divide both sides by -15

Left Hand Side:

Right Hand Side:

Our result is:

 

Example Question #12 : How To Find The Solution For A System Of Equations

Find the solutions for the following set of equations:

 

Possible Answers:

Correct answer:

Explanation:

If we multiply both sides of our bottom equation by , we get . We can now add our two equations, and eliminate , leaving only one variable. When we add the equations, we get . Therefore, . Finally, we go back to either of our equations, and plug in  so we can solve for .

 

Example Question #41 : How To Find The Solution For A System Of Equations

Give the solution to the system of equations below.

 

Possible Answers:

No solution

Correct answer:

Explanation:

Solve the second equation for , allowing us to solve using the substitution method.

Substitute for   in the first equation, and solve for .

Now, substitute for  in either equation; we will choose the second. This allows us to solve for .

Now we can write the solution in the notation , or .

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