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Zorluk: ZorSolving Systems of Linear Equations

Given the system of equations below, what is the value of the expression x−2yx - 2y?

5x−13=4y5x - 13 = 4y
2x+y=132x + y = 13
  1. -1Cevap
  2. B
    -16
  3. C
    -13
  4. D
    11

Cevap

The correct value of the expression is -1.
Solving the system of equations by rearranging and using elimination yields the solution x = 5 and y = 3. Substituting these values into the target expression x - 2y gives 5 - 2(3), which evaluates to 5 - 6 = -1.

Adım Adım Çözüm

1
Rearrange the first equation into standard form to align the variables.
5x−4y=135x - 4y = 13
Aligning the variables vertically makes it much easier to use the elimination method.
2
Multiply the entire second equation by 4.
8x+4y=528x + 4y = 52
This creates opposite coefficients (-4y and +4y) so the y variable will cancel out when the equations are added.
3
Add the rearranged first equation and the modified second equation together.
(5x−4y)+(8x+4y)=13+52⇒13x=65⇒x=5(5x - 4y) + (8x + 4y) = 13 + 52 \Rightarrow 13x = 65 \Rightarrow x = 5
Eliminating y isolates x, allowing us to find its numerical value.
4
Substitute x = 5 back into the original second equation to solve for y.
2(5)+y=13⇒10+y=13⇒y=32(5) + y = 13 \Rightarrow 10 + y = 13 \Rightarrow y = 3
This completes the solution pair (x, y) for the system of equations.
5
Substitute x = 5 and y = 3 into the requested expression x−2yx - 2y.
5−2(3)=5−6=−15 - 2(3) = 5 - 6 = -1
The question asks for the evaluated value of this specific expression, not just the solution coordinates.

Anahtar Kavram

Solving Systems of Linear Equations using elimination or substitution, followed by algebraic evaluation.
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Konular

Solving Systems of Linear Equations

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