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Home :: Contents (2267) :: Algebra (377) :: Systems of Equations

Systems of Equations (43 problems)


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Problem #1: 2x2 System of Equations

Solve the following systems by the addition method:

4x – 5y = 20
y = 4/5x – 4
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Problem #2: 2x2 System of Equations

Solve the following system by graphing:

x – 2y = -6
y = -3x/2 – 1
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Problem #3: 2x2 System of Equations
Solve the following systems of inequalities: x – y > 1
x - y < 3
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Problem #4: 2x2 System of Equations

Solve the system by the addition (elimination) method:

2x + 4y = -24
x - 4y = 18
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Problem #5: 2x2 System of Equations
Solve the following equations:

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Problem #6: 2x2 System of Equations

Solve the following systems by the substitution method:

x – 2y = 0
4x – 8y = 0
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Problem #7: 2x2 System of Equations

Solve the system by the substitution method. Determine whether the equations are independent, dependent, or inconsistent.

2y = x + 6 and
-3x + 2y = -2

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Problem #8: 2x2 System of Equations
Solve the following system of equations using substitution: -x + 3y = 10
2x + 8y = -6
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Problem #9: 2x2 System of Equations

Solve the following systems by the substitution method:

7x – 4y = 26
y = x – 5
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Problem #10: 2x2 System of Equations

Solve the following systems by the addition method:

x + 2y = 4
3x – 6y = 6
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Problem #11: 2x2 System of Equations

In Lewis Carroll’s Through the Looking Glass, the following dialogue takes place:

Tweedledum (to Tweedledee): The sum of your weight and twice mine is 361 pounds.

Tweedledee (to Tweedledum): Contrawise, the sum of your weight and twice mine is 362 pounds.

Find the weight of each of the two characters.


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Problem #12: 2x2 System of Equations
Solve the following system of equations by the addition method: 5x + 2y = -7
x + 3y = 9
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Problem #13: 2x2 System of Equations

Solve the following system of equations for x and y:

5x + 3y = 7

2x - 3y = 14

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Problem #14: 2x2 System of Equations

Solve the system:

x + y = -5
2x - y = -7
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Problem #15: 2x2 System of Equations

Sally bought three chocolate bars and a pack of gum and paid $1.75. Jake bought two chocolate bars and four packs of gum and paid $2.00. Find the cost of a chocolate bar and the cost of a pack of gum.

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Problem #16: 2x2 System of Equations

Solve the system by substitution:

y = 2x - 6
y = 3x
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Problem #17: 2x2 System of Equations

Solve the system using the graphing method:

x + y = 2
-4y = 4x – 12
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Problem #18: 2x2 System of Equations

If the sum of a number and 9 is decreased by 81, the result is 54. Find the number.

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Problem #19: 2x2 System of Equations
Solve the system of equations using the graphing method: 5x – y = 10
2x + y = 4
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Problem #20: 2x2 System of Equations

Of the $50,000 that Natasha pocketed on her last real estate deal, $20,000 went to charity. She invested part of the remainder in Dreyfus New Leaders Fund with an annual yield of 16% and the rest in Templeton Growth Fund with an annual yield of 25%. If she made $6060 on these investments in 1 year, then how much did she invest in each fund? Of the $50,000 that Natasha pocketed on her last real estate deal, $20,000 went to charity. She invested part of the remainder in Dreyfus New Leaders Fund with an annual yield of 16% and the rest in Templeton Growth Fund with an annual yield of 25%. If she made $6060 on these investments in 1 year, then how much did she invest in each fund?

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