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Zorluk: OrtaSolving Systems of Linear Equations

Determine the exact ordered pair (x,y)(x, y) that satisfies the system of linear equations shown below.

4x−3y=254x - 3y = 25
x+2y=9x + 2y = 9

Enter your answer in the format (x,y)(x, y).

Cevap: (7, 1) / (7,1) / 7, 1 / 7,1

Cevap

The correct ordered pair is (7, 1).
The correct solution is (7, 1). To verify, substitute x = 7 and y = 1 into both original equations. For the first equation: 4(7) - 3(1) = 28 - 3 = 25. For the second equation: 7 + 2(1) = 7 + 2 = 9. Since both equations hold true simultaneously, (7, 1) is the accurate solution.

Adım Adım Çözüm

1
Isolate the variable xx in the second equation.
x=9−2yx = 9 - 2y
The second equation has an xx with a coefficient of 1, making it the most straightforward variable to isolate for substitution without creating fractions.
2
Substitute the expression for xx into the first equation.
4(9−2y)−3y=254(9 - 2y) - 3y = 25
This creates a single equation containing only the variable yy, which can be solved algebraically.
3
Distribute the 4 and combine like terms.
36−8y−3y=25⇒36−11y=2536 - 8y - 3y = 25 \Rightarrow 36 - 11y = 25
Simplifying the equation prepares it for isolating the yy term.
4
Solve for yy by subtracting 36 from both sides and dividing by -11.
−11y=−11⇒y=1-11y = -11 \Rightarrow y = 1
This determines the numerical value for the y-coordinate of the solution.
5
Substitute y=1y = 1 back into the isolated xx equation from Step 1.
x=9−2(1)⇒x=9−2=7x = 9 - 2(1) \Rightarrow x = 9 - 2 = 7
This provides the corresponding x-coordinate to complete the ordered pair.

Anahtar Kavram

Solving Systems of Linear Equations by Substitution
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Konular

Solving Systems of Linear Equations

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