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Difficulty: EasySystems of Linear Equations

The variables xx and yy satisfy the system of equations below.

y=10−2xy = 10 - 2x
3x−y=53x - y = 5

What is the value of xx?

  1. A
    15
  2. B
    4
  3. 3Answer
  4. D
    1

Answer

3
Substituting the expression for yy from the first equation, 10−2x10 - 2x, into the second equation yields 3x−(10−2x)=53x - (10 - 2x) = 5. Distributing the negative sign results in 3x−10+2x=53x - 10 + 2x = 5. Combining the like terms of xx gives 5x−10=55x - 10 = 5. Adding 10 to both sides of the equation results in 5x=155x = 15. Finally, dividing both sides by 5 gives x=3x = 3.

Step-by-Step Solution

1
Substitute the expression for yy from the first equation into the second equation.
3x−(10−2x)=53x - (10 - 2x) = 5
To eliminate the variable yy and obtain a single linear equation in terms of xx.
2
Distribute the negative sign through the parentheses and combine like terms.
3x−10+2x=53x - 10 + 2x = 5, which simplifies to 5x−10=55x - 10 = 5
To simplify the linear equation before isolating the variable.
3
Isolate the variable xx by adding 10 to both sides and then dividing by 5.
5x=155x = 15, which gives x=3x = 3
To determine the value of xx.

Key Concept

Solving systems of linear equations using substitution
Estimated Time:45s
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Topics

Systems of Linear Equations

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