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Difficulty: EasySolving Systems of Linear Equations

Find the ordered pair (x,y)(x, y) that satisfies both equations below:

y=3x−2y = 3x - 2
y=x+6y = x + 6

Which of the following is the correct solution?

  1. (4,10)(4, 10)Answer
  2. B
    (2,8)(2, 8)
  3. C
    (8,14)(8, 14)
  4. D
    (4,14)(4, 14)

Answer

The correct solution is the ordered pair (4,10)(4, 10).
By setting the two expressions for y equal to each other (3x−2=x+63x - 2 = x + 6), we can isolate x to find x=4x = 4. Substituting 44 back into either original equation gives y=10y = 10. Therefore, the solution is (4,10)(4, 10).

Step-by-Step Solution

1
Set the right sides of both equations equal to each other.
3x−2=x+63x - 2 = x + 6
Since both expressions are equal to y, they must be equal to each other.
2
Subtract xx from both sides to group the variables.
2x−2=62x - 2 = 6
This begins the process of isolating the variable x.
3
Add 22 to both sides of the equation.
2x=82x = 8
This isolates the term with the x variable on one side and the constant on the other.
4
Divide both sides by 22.
x=4x = 4
This fully isolates x to find its numerical value.
5
Substitute x=4x = 4 into the second equation to find yy.
y=4+6=10y = 4 + 6 = 10
Substituting the known x value back into either original equation yields the corresponding y value.

Key Concept

Solving systems of linear equations using the substitution method.
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Topics

Solving Systems of Linear Equations

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