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Difficulty: EasySystems of Linear Equations
In a science experiment, the temperature yy, in degrees Celsius, and the time xx, in minutes, are related by a system of equations. The relationships are given by:
y=2x−3y = 2x - 3
3x−y=83x - y = 8
What is the value of xx in the solution to this system?
  1. A
    1
  2. 5Answer
  3. C
    7
  4. D
    11

Answer

5
The correct answer is 5. Substituting the expression for yy from the first equation into the second equation yields 3x−(2x−3)=83x - (2x - 3) = 8. Distributing the negative sign results in 3x−2x+3=83x - 2x + 3 = 8. Combining the variable terms gives x+3=8x + 3 = 8. Subtracting 3 from both sides isolates xx, giving x=5x = 5.

Step-by-Step Solution

1
Substitute the expression for yy from the first equation, y=2x−3y = 2x - 3, into the second equation.
3x−(2x−3)=83x - (2x - 3) = 8
This eliminates the variable yy so the equation can be solved directly for xx.
2
Distribute the negative sign to both terms inside the parentheses.
3x−2x+3=83x - 2x + 3 = 8
Distributing the negative sign to both 2x2x and −3-3 simplifies the expression correctly.
3
Combine like terms on the left side of the equation.
x+3=8x + 3 = 8
Subtracting 2x2x from 3x3x leaves a single xx term.
4
Subtract 3 from both sides of the equation to isolate xx.
x=5x = 5
This isolates the variable xx to find the final solution.

Key Concept

Solving systems of linear equations using substitution
Estimated Time:1m 0s
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Topics

Systems of Linear Equations

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