Target question: What is the value of \(8x + y\)?

Statement 1: \(3x – 2y + z = 10\)
Notice that z can have infinitely many values, and each of those z-values will change the values of x and y, making it impossible to answer the target question
Statement 1 is NOT SUFFICIENT

Statement 2: \(2(x + 3y) – (y + 2z) = –25\)
When we apply the same logic we applied for statement 1, we can conclude that statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
From the two statements we have the following system pf equations:
(1) \(3x – 2y + z = 10\)
(2) \(2(x + 3y) – (y + 2z) = –25\)

Simplify equation (2) as follows:
(1) \(3x – 2y + z = 10\)
(2) \(2x + 5y - 2z = –25\)

In order to eliminate the z-terms, let's take equation (1) and multiply both sides by 2 to get the following equivalent equation:
(1) \(6x – 4y + 2z = 20\)
(2) \(2x + 5y - 2z = –25\)

From here, something nice happens when we add the two equations.
We get: \(8x + y = -5\)
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent
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Simpler one:

3x–2y+z=10 ---> (eq1)
3 variable, one equation. Can't solve for 8x+y


2(x+3y)–(y+2z)=–25
2x+6y–y+2z=–25
2x+5y+2z=–25 ---> (eq2)
Here also, 3 variable, one equation. Hence, can't solve for 8x+y.

Using both,
2*(eq1) + (eq2) gives me,
8x + y = 5

Hence, C.

It should be 8x + y =- 5 though, no?

20+ (-25)=-5

Posted from my mobile device

Good catch, thanks!
I've edited my response.

Kudos for you!
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Hi Brent, the last part above is creating confusion both statements together are sufficient right?

Sorry about that.
Yes, the statements combined are sufficient, which means the answer is C
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