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avatar+68 

What is the ordered pair of real numbers\((x, y)\)which satisfies the equation \(|x+ y-7|+ |4x - y+ 12|= 0\)?

 Mar 20, 2024

Best Answer 

 #2
avatar+394 
+2

For two absolute values to sum to zero, we must have 

\(|a|+|b|=0\), then \(\begin{cases} a = 0 \\ b = 0 \end{cases}\), because \(|x|\ge0\).

Following this logic, the only possible solution is \(\begin{cases} x + y - 7 = 0 \\ 4x - y + 12 = 0 \end{cases}\).

 \(5x+5=0\)

\(\begin{cases} x = -1\\y=8 \end{cases}\).

Therefore the ordered pair (-1, 8) is the only ordered pair that works.

 Mar 21, 2024
 #1
avatar+1351 
-1

When we graph the equations, we see that they intersect at (4,2).  Therefore, the solution is (4,2).

 

 Mar 20, 2024
 #2
avatar+394 
+2
Best Answer

For two absolute values to sum to zero, we must have 

\(|a|+|b|=0\), then \(\begin{cases} a = 0 \\ b = 0 \end{cases}\), because \(|x|\ge0\).

Following this logic, the only possible solution is \(\begin{cases} x + y - 7 = 0 \\ 4x - y + 12 = 0 \end{cases}\).

 \(5x+5=0\)

\(\begin{cases} x = -1\\y=8 \end{cases}\).

Therefore the ordered pair (-1, 8) is the only ordered pair that works.

hairyberry Mar 21, 2024

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