+118 What is the ordered pair of real numbers\((x, y)\)which satisfies the equation \(|x+ y-7|+ |4x - y+ 12|= 0\)?
+399 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.
+2653 When we graph the equations, we see that they intersect at (4,2). Therefore, the solution is (4,2).
+399 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.
