Question

which of the following equation when paired with x+y=4 makes the system consistent with a unique solution?

Answer 1

Answer:

For unique solution:-

a1/a2 not equal to b1 /b2

x+y =4

coefficient of x and y are 1

So, 2x+3y=9

Answer 2

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With x + y = 4 makes the system consistent

with a unique solution ?

(a) 21x-y=2

(b) x +y = 6

(C) 3x + 3y = 12 (d) 6x+6y = 40​

Concept:

One of the key techniques used to solve an equation system is Cramer's rule. The determinants of matrices are used in this method to derive the values of the system's variables. Thus, the determinant technique is another name for Cramer's rule.

Given:

X+Y=4

Find:

With x + y = 4 makes the system consistent

with a unique solution ?

(a) 21x-y=2

(b) x +y = 6

(C) 3x + 3y = 12

(d) 6x+6y = 40​

Solution:

For unique solution:-

a1/a2 not equal to b1 /b2

a)21x-y=2

  21/1≠-1/1

So this has a uniques solution.

b) x+y=6

1/1 =1/1

SO. this has a infinite solution

c) 3x+3y=12

3/1=3/1

So, this has a infinte solution.

d)6x+6y=40

6/1=6/1

So, this has infinite solution.

Therefore, option A is correct.

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