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Zorluk: OrtaSolving Systems of Linear Equations

The two linear equations below form a system.

2x+3y=122x + 3y = 12
2x−y=42x - y = 4

Based on the solution to this system, what is the value of the expression x+2yx + 2y?

  1. A
    5
  2. 7Cevap
  3. C
    10
  4. D
    12

Cevap

The correct answer is 7.
The correct answer is found by first solving the system of equations. Subtracting the second equation from the first eliminates the x variable, giving 3y - (-y) = 12 - 4, which simplifies to 4y = 8 and y = 2. Substituting y = 2 into the second equation yields 2x - 2 = 4, meaning 2x = 6 and x = 3. Finally, evaluating the expression x + 2y with these values gives 3 + 2(2) = 3 + 4 = 7.

Adım Adım Çözüm

1
Eliminate the x variable by subtracting the second equation from the first.
(2x−2x)+(3y−(−y))=12−4⇒4y=8(2x - 2x) + (3y - (-y)) = 12 - 4 \Rightarrow 4y = 8
Because the coefficient of x is identical in both equations, subtracting them cancels out the x terms entirely, leaving an equation with only y.
2
Solve for y.
y=2y = 2
Dividing both sides of the equation by 4 isolates the y variable.
3
Substitute the value of y back into the second equation to solve for x.
2x−(2)=4⇒2x=6⇒x=32x - (2) = 4 \Rightarrow 2x = 6 \Rightarrow x = 3
Using the known value of y allows us to find the corresponding x value for the system's ordered pair.
4
Evaluate the target expression x+2yx + 2y using the found values.
3+2(2)=3+4=73 + 2(2) = 3 + 4 = 7
This answers the specific question asked in the stem by applying the solution to the given expression.

Anahtar Kavram

Solving Systems of Linear Equations by Elimination
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Konular

Solving Systems of Linear Equations

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