### All GRE Subject Test: Math Resources

## Example Questions

### Example Question #1 : Solving Systems Of Equations

Solve the system of equations.

**Possible Answers:**

**Correct answer:**

The easiest way to solve this question is to use substitution. Since you can replace y for 7x-2 in the other equation.

You should have

.

Distribute the 2 to the parentheses.

Add 4 to both sides of the equation.

Subtract 6x from both sides.

Divide by 8 to get x.

Put 1 back in to either equation for x to solve for y.

### Example Question #1 : Solving Systems Of Equations

Solve the system of equations.

**Possible Answers:**

**Correct answer:**

First task is to solve at least one of the equations for y.

Move -3x to the other side by adding 3x to both sides.

Divide by 2 to all the terms in the equation.

Plug this value for y into the other equation.

Distribute the 2.

Add 3x to both sides.

Subtract 19 from both sides of the equation.

Divide by 6.

Plug this back in for x in either equation.

### Example Question #2 : Solving Systems Of Equations

Solve each system of equations.

**Possible Answers:**

**Correct answer:**

To solve this system of equations, you are given the value of .

The second equation is

So you put the value of into the second equation.

Combine like terms.

Add to both sides of the equation.

Divide both sides by .

Substitute the value of x in one of the equations to get the value of y.

is the correct answer.

### Example Question #4 : Solving Systems Of Equations

Solve the system of equations.

**Possible Answers:**

**Correct answer:**

To cancel out the terms, multiply by

Then add:

______________________

Plug the value of which is into one of the equations to get the value of .

is the correct answer.

### Example Question #5 : Solving Systems Of Equations

Solve each system of equations.

**Possible Answers:**

**Correct answer:**

Using the substitution method, set the two systems of equations equal to each other.

Isolate the variable by subtracting from both sides of the equation.

To get the value of , substitute the value of in one of the equations.

is the correct answer.

### Example Question #3 : Solving Systems Of Equations

Solve each system of equations.

**Possible Answers:**

**Correct answer:**

Using the substitution method, set both systems of equations equal to each other.

Isolate the variable by adding to both sides of the equation.

Add to both sides.

Divide both sides by 3.

To get the value of y, substitute the value of x in one of the equations.

is the correct answer.

### Example Question #7 : Solving Systems Of Equations

Solve the systems of equations.

**Possible Answers:**

**Correct answer:**

In order to eliminate the terms, first multiply the first equation by

Then multiply the second equation by

This will now eliminate the terms when added together.

+

_________________________

Divide both sides by

Now substitute the value of which is to get the value of in one of the the two original equations.

Add to both sides of the equation.

Divide both sides by

is the correct answer.

### Example Question #8 : Solving Systems Of Equations

Solve this system of equations:

**Possible Answers:**

**Correct answer:**

Set both equations equal to each other and solve.

Add to both sides of the equation.

Add to both sides of the equation.

Divide both sides by 8.

Plug the value of the variable into one of the equations to get the value of

is the correct answer for this system of equations.

### Example Question #9 : Solving Systems Of Equations

Solve this system of equations:

**Possible Answers:**

**Correct answer:**

To solve this system of equations, multiply the first equation by .

Now add the two equations together to remove the terms.

+

_____________________________

Divide both sides by .

Plug the value of the variable, which is into one of the equations.

Subtract from both sides of the equation.

Divide both sides by

is the correct answer for this system of equations.

### Example Question #4 : Solving Systems Of Equations

Solve this system of equations:

**Possible Answers:**

**Correct answer:**

To solve this system of equations:

Multiply the first equation by and the second equation by .

Add these two equations; this will remove the terms.

+

___________________

To get the value of , plug the value of , which is into one of the equations.

Divide both sides by

is the correct answer for this system of equations.

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