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Zorluk: KolaySystems of Linear Equations

In the system of linear equations shown below, what value of xx satisfies both equations?

y=2x−5y = 2x - 5
3x−2y=123x - 2y = 12
  1. A
    −22-22
  2. −2-2Cevap
  3. C
    22
  4. D
    −9-9

Cevap

−2-2
To find the value of xx, substitute the expression for yy from the first equation, y=2x−5y = 2x - 5, into the second equation, 3x−2y=123x - 2y = 12. This yields 3x−2(2x−5)=123x - 2(2x - 5) = 12. Distributing the −2-2 across the terms in the parentheses results in 3x−4x+10=123x - 4x + 10 = 12. Simplifying the left side of the equation by combining like terms gives −x+10=12-x + 10 = 12. Subtracting 1010 from both sides results in −x=2-x = 2. Finally, multiplying or dividing both sides by −1-1 yields x=−2x = -2.

Adım Adım Çözüm

1
Substitute the expression for yy from the first equation into the second equation
3x−2(2x−5)=123x - 2(2x - 5) = 12
To eliminate yy and obtain an equation containing only xx.
2
Distribute −2-2 to the terms inside the parentheses
3x−4x+10=123x - 4x + 10 = 12
To remove parentheses and prepare the equation for simplifying.
3
Combine like terms and solve for xx
−x+10=12-x + 10 = 12, which gives −x=2-x = 2, and thus x=−2x = -2
To isolate and find the value of xx.

Anahtar Kavram

Solving systems of linear equations using substitution
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Konular

Systems of Linear Equations

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