What is the value of x?

1, 4x = 2Y-6
2X-Y + 3 = 0
2X - Y = -3
IS
2, Y-3 = 2X
2X-Y = 3
x = 1 or x = 2
IS
3, On solving two equations
2x - y = 9
IS
E

Statement 1: Value of "Y" is unkwown. x= 2y-6/4 . Insufficient
Statement 2" Value of "Y" is unkwown. x=y-3/2 . Insufficient
Now to check if option C is valid and whether we can find "x" with both statements together . Comparing both the linear equations we find a1/a2=b1/b2=c1/c2 i.e 4/2=2/1=6/3 .This condition indicates that equation has no solution.
Answer: E

What is the value of x?

\((1)\)\(4x = 2y − 6\)

We cannot determine the value of x as we are un-aware of the value of y neither it can be computed with given equation.

Hence, (1) ===== is NOT SUFFICIENT

\((2) (y - 3)/2 = x\)

We cannot determine the value of x as we are un-aware of the value of y neither it can be computed with given equation.

Hence, (2) ===== is NOT SUFFICIENT

Combining (1) & (2)

Lets substitute value of (2) in (1)

\(\frac{(y - 3)}{2} = x\) =====> (2)

\(4x = 2y − 6\) =====> (1)

\(4 * \frac{(y-3)}{2} = 2y - 6\)

\(2 * (y-3) = 2y - 6\)

\(2y - 6 = 2y - 6\)

As both the sides of the equation are same, we cannot determine the value of the x

Hence, (1) & (2) ===== is NOT SUFFICIENT


Hence, Answer is E

Both the equations are same. hence E

Target question: What is the value of x?

Key concept #1: It's impossible to solve a linear equation with two variables (with no restrictions on the values of the variables) for one of the variables.

Statement 1: 4x = 2y − 6
Since this is a linear equation with two variables, we can't solve it for x
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: (y - 3)/2 = x
Since this is a linear equation with two variables, we can't solve it for x
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Key concept #2: We can solve a system of two linear equations with two variables as long as the two equations are different
In this case, the two equations given in statements 1 and 2 are equivalent. Here's why:
Take the equation from statement 2: (y - 3)/2 = x
Multiply both sides of the equation by 2 to get: y - 3 = 2x
Multiply both sides of the equation by 2 to get: 2y - 6 = 4x, which is identical to the equation given and statement 1.

So, we basically have just 1 unique linear equation with two variables, which means we can't solve it for x.
Since we can’t answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent