# GRE Subject Test: Math : Solving Systems of Equations

## Example Questions

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### Example Question #1 : Systems Of Equations

Solve the system of equations.

Explanation:

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 #2 : Systems Of Equations

Solve the system of equations.

Explanation:

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.

Subtract 19 from both sides of the equation.

Divide by 6.

Plug this back in for x in either equation.

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

Solve each system of equations.

Explanation:

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.

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

Solve the system of equations.

Explanation:

To cancel out the  terms, multiply  by

______________________

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

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

Solve each system of equations.

Explanation:

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.

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

Solve each system of equations.

Explanation:

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

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

Divide both sides by 3.

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

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

Solve the systems of equations.

Explanation:

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

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

Solve this system of equations:

Explanation:

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 #301 : Algebra

Solve this system of equations:

Explanation:

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 #10 : Systems Of Equations

Solve this system of equations:

Explanation:

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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