+0

# Absolute Value

0
5
3
+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

#2
+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
+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
+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.

hairyberry Mar 21, 2024