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Zorluk: OrtaSolving Systems of Linear Equations

Given the system of linear equations below, what is the value of yy?

5x+2y=125x + 2y = 12
3x−4y=23x - 4y = 2
  1. A
    2
  2. B
    11
  3. 1Cevap
  4. D
    -2

Cevap

The correct value for y is 1.
By multiplying the first equation by 2, we get 10x + 4y = 24. Adding this to the second equation (3x - 4y = 2) eliminates y, resulting in 13x = 26, which simplifies to x = 2. Substituting x = 2 back into the first equation gives 5(2) + 2y = 12, or 10 + 2y = 12. Subtracting 10 from both sides leaves 2y = 2, yielding the final correct answer of y = 1.

Adım Adım Çözüm

1
Multiply the first equation by 2 to align the coefficients of y for elimination.
10x+4y=2410x + 4y = 24
Creating a +4y term in the first equation allows y to be eliminated when added to the -4y term in the second equation.
2
Add the modified first equation to the second equation.
(10x+3x)+(4y−4y)=24+2⇒13x=26(10x + 3x) + (4y - 4y) = 24 + 2 \Rightarrow 13x = 26
This eliminates the variable y, leaving a single-variable equation that can be easily solved for x.
3
Divide both sides by 13 to solve for x.
x=2x = 2
Isolating x provides the first part of the coordinate solution.
4
Substitute x = 2 back into the first original equation to solve for y.
5(2)+2y=12⇒10+2y=12⇒2y=2⇒y=15(2) + 2y = 12 \Rightarrow 10 + 2y = 12 \Rightarrow 2y = 2 \Rightarrow y = 1
Since the question asks specifically for the value of y, this final substitution step is required.

Anahtar Kavram

Solving Systems of Linear Equations using the Elimination Method
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Konular

Solving Systems of Linear Equations

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