Question

check whether the given pair of equations represents consistent or inconsistent find the solution if the equation are consistent 3x+4y=10 and 4x-3y=5​

Answer 1

Given data:

The two given equations are

• 3x + 4y = 10
• 4x - 3y = 5

To find:

• whether the given pair of equations represents consistent or inconsistent system of equations
• if consistent, the solution

Step-by-step explanation:

The given equations are

• 3x + 4y = 10 . . . . . (1)
• 4x - 3y = 5 . . . . . (2)

We see that, 3/4 ≠ 4/(- 3). Thus the system of equations is consistent.

We can get a solution. Let us try with method of elimination.

Multiply equation (1) by 4 and equation (2) by 3. We get

• 12x + 16y = 40
• 12x - 9y = 15

On subtraction, we get

• 25y = 25, i.e., y = 1

Putting y = 1 in (1), we get

• 3x + 4 = 10
• or, 3x = 6
• or, x = 2

Therefore the required solution is x = 2, y = 1.

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Solve faster using elimination method.

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Solve the pair of equations by method of elimination by equating coefficients:

3 - (x - 5) = y + 4 and 2 (x + y) = 4 - 3y

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