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GRE Subject Test: Math : Systems of Equations

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Example Question #1 : Solving Systems Of Equations

2y=6x+4

y=7x-2

Solve the system of equations.

Possible Answers:

x=-1, y=3

x=4, y=8

x=-2, y=-3

$x=-8, y=\frac{1}{2}$

x=1, y=5

Correct answer:

x=1, y=5

Explanation:

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

You should have

2(7x-2)=6x+4 .

Distribute the 2 to the parentheses.

14x-4=6x+4

Add 4 to both sides of the equation.

14x=6x+8

Subtract 6x from both sides.

8x=8

Divide by 8 to get x.

x=1

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

y=3(1)+2

y=5

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Example Question #2 : Solving Systems Of Equations

-3x+2y=19

-3x-19=2y

Solve the system of equations.

Possible Answers:

$x=-\frac{1}{5}, y=2\frac{1}{4}$

$x=\frac{1}{4}, y=-2\frac{1}{5}$

$x=-1, y=-4\frac{1}{3}$

$x=-6\frac{1}{3}, y=0$

$x=3, y=-4\frac{1}{5}$

Correct answer:

$x=-6\frac{1}{3}, y=0$

Explanation:

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

-3x+2y=19

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

2y=3x+19

Divide by 2 to all the terms in the equation.

$y=\frac{3}{2}x+\frac{19}{2}$

Plug this value for y into the other equation.

$-3x-19=2(\frac{3}{2}x+\frac{19}{2})$

Distribute the 2.

-3x-19=3x+19

Add 3x to both sides.

-19=6x+19

Subtract 19 from both sides of the equation.

-38=6x

Divide by 6.

$x=-6.33 or -6\frac{1}{3}$

Plug this back in for x in either equation.

-3(-6.33)+2y=19

19+2y=19

2y=0

y=0

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Example Question #1 : Systems Of Equations

Solve each system of equations.

y = 2x-16

y + 3x = 9

Possible Answers:

(-5,6)

(-5,-6)

(5,-6)

(5,6)

Correct answer:

(5,-6)

Explanation:

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

y = 2x - 16

The second equation is y + 3x = 9

So you put the value of into the second equation.

2x-16 + 3x = 9

Combine like terms.

5x -16 = 9

Add to both sides of the equation.

5x - 16 + 16 = 9 + 16

5x = 25

Divide both sides by .

$\frac{5x}{5} = \frac{25}{5}$

x = 5

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

y = 2(5) - 16

y = 10-16

y = -6

(5,-6) is the correct answer.

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Example Question #1 : Systems Of Equations

Solve the system of equations.

x + y = 5

2x - 3y =5

Possible Answers:

(4, 1)

(-4, -1)

(4, -1)

(1,4)

Correct answer:

(4, 1)

Explanation:

x + y = 5

2x-3y = 5

To cancel out the terms, multiply x + y = 5 by

-2x - 2y = -10

Then add:

2x-3y = 5

______________________

-5y = -5

y = 1

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

x + 1 = 5

x+1-1 = 5 - 1

x = 4

(4,1) is the correct answer.

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Example Question #1 : Solving Systems Of Equations

Solve each system of equations.

y = 6x

y = x-15

Possible Answers:

(18,3)

(-3,-18)

(-18,-3)

(3,18)

Correct answer:

(-3,-18)

Explanation:

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

6x = x-15

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

6x-x = x-x-15

5x = -15

$\frac{5x}{5} = \frac{-15}{5}$

x = -3

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

y = 6(-3)

y = -18

(-3,-18) is the correct answer.

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Example Question #1 : Systems Of Equations

Solve each system of equations.

y = -x + 6

y = 2x-3

Possible Answers:

(-3,-3)

(3,-3)

(3,3)

(-3,3)

Correct answer:

(3,3)

Explanation:

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

-x + 6 = 2x - 3

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

-x + x + 6 = 2x + x -3

6 = 3x - 3

Add to both sides.

9 = 3x

Divide both sides by 3.

$\frac{9}{3} =\frac{3x}{3}$

3 = x

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

2 (3) - 3 = 6 - 3 = 3

y = 3

(3,3) is the correct answer.

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Example Question #1 : Solving Systems Of Equations

Solve the systems of equations.

-5x + 10 y = 60

-4x + 16y = 32

Possible Answers:

(-2,-16)

(16,2)

(-2,16)

(-16,-2)

Correct answer:

(-16,-2)

Explanation:

In order to eliminate the terms, first multiply the first equation by -4.

-4 (-5x+10y) = (-4) 60

20x - 40y = -240

Then multiply the second equation by

5 (-4x + 16y) = 5 (32)

-20 x +80y = 160

This will now eliminate the terms when added together.

20x - 40y = -240

+ -20 x +80y = 160

_________________________

40y = -80

Divide both sides by 40.

y = -2

Now substitute the value of which is -2, to get the value of in one of the the two original equations.

-5x-20 = 60

Add to both sides of the equation.

-5x -20 + 20 = 60 + 20

-5x = 80

Divide both sides by -5.

$80 \div -5 = -16$

x = -16

(-16,-2) is the correct answer.

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Example Question #1 : Systems Of Equations

Solve this system of equations:

y = -5x +2

y = 3x-14

Possible Answers:

(-8,2)

(8,2)

(2,-8)

(2,8)

Correct answer:

(2,-8)

Explanation:

Set both equations equal to each other and solve.

-5x + 2 = 3x - 14

Add to both sides of the equation.

-5x + 5x + 2 = 3x + 5x - 14

2 = 8x - 14

Add to both sides of the equation.

2+14 = 8x-14+14

16 = 8x

Divide both sides by 8.

x = 2

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

-5(2) + 2 = y

-10 +2 =-8

y = -8

(2,-8) is the correct answer for this system of equations.

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Example Question #1 : Solving Systems Of Equations

Solve this system of equations:

3.5x + 2.5y = 38

1.5x -7.5y = -18

Possible Answers:

(8,4)

(-4,8)

(4,8)

(-8,4)

Correct answer:

(8,4)

Explanation:

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

3 (3.5x + 2.5y) =38 (3)

10.5x +7.5y = 114

Now add the two equations together to remove the terms.

10.5x +7.5y = 114

+ 1.5x -7.5y = -18

_____________________________

12.0x = 96

Divide both sides by .

$96\div12 = 8$

x = 8

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

3.5(8) + 2.5y = 38

28 + 2.5y = 38

Subtract from both sides of the equation.

28-28 + 2.5y = 38-28

2.5y = 10

Divide both sides by 2.5

y = 4

(8,4) is the correct answer for this system of equations.

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Example Question #121 : Linear Algebra

Solve this system of equations:

$-\frac{1}{2}x - \frac{1}{4}y =3$

$-\frac{1}{3}x +\frac{1}{6}y = 2$

Possible Answers:

(0,-6)

(-6,0)

(6,0)

(0,6)

Correct answer:

(-6,0)

Explanation:

To solve this system of equations:

$-\frac{1}{3}x +\frac{1}{6}y = 2$

Multiply the first equation by and the second equation by .

$4 (-\frac{1}{2}x -\frac{1}{4}y) = 3(4)$

-2x -y =12

$-6 (-\frac{1}{3}x+\frac{1}{6} y) = (-6) 2$

2x-y = -12

Add these two equations; this will remove the terms.

-2x -y =12

+ 2x-y = -12

___________________

-2y = 0

y = 0

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

2x -y = -12

2x - 0 = -12

2x = -12

Divide both sides by

$\frac{2x}{2} = \frac{-12}{2}$

x = -6

(-6,0) is the correct answer for this system of equations.

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GRE Subject Test: Math : Systems of Equations

Study concepts, example questions & explanations for GRE Subject Test: Math

All GRE Subject Test: Math Resources

Example Questions

Example Question #1 : Solving Systems Of Equations

Example Question #2 : Solving Systems Of Equations

Example Question #1 : Systems Of Equations

Example Question #1 : Systems Of Equations

Example Question #1 : Solving Systems Of Equations

Example Question #1 : Systems Of Equations

Example Question #1 : Solving Systems Of Equations

Example Question #1 : Systems Of Equations

Example Question #1 : Solving Systems Of Equations

Example Question #121 : Linear Algebra

All GRE Subject Test: Math Resources

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