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Difficulty: EasySolving Systems of Linear Equations

Which ordered pair (x,y)(x, y) is the solution to the following system of linear equations?

3x+y=173x + y = 17
x−y=3x - y = 3
  1. (5,2)(5, 2)Answer
  2. B
    (2,5)(2, 5)
  3. C
    (5,8)(5, 8)
  4. D
    (20,17)(20, 17)

Answer

The correct solution is the ordered pair (5,2)(5, 2).
The correct answer is (5, 2). By adding the two equations, the y terms cancel each other out, leaving 4x = 20. Dividing both sides by 4 gives x = 5. Substituting this value back into the second equation (5 - y = 3) allows us to solve for y, which is 2.

Step-by-Step Solution

1
Add the two equations together to eliminate the y variable.
(3x+y)+(x−y)=17+3⇒4x=20(3x + y) + (x - y) = 17 + 3 \Rightarrow 4x = 20
Since the coefficients of y are opposites (1 and -1), adding the equations cancels out the y terms.
2
Solve for x by dividing both sides of the resulting equation by 4.
x=5x = 5
Dividing by the coefficient of x isolates the variable.
3
Substitute the value of x back into the second original equation.
5−y=35 - y = 3
Substituting the known x value leaves an equation with only one variable, y.
4
Solve for y.
−y=3−5⇒−y=−2⇒y=2-y = 3 - 5 \Rightarrow -y = -2 \Rightarrow y = 2
Isolating y provides the final part of the solution.

Key Concept

Solving systems of linear equations using the elimination method
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Topics

Solving Systems of Linear Equations

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