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Absolute Value

0

37

3

+118

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

SilviaJendeukie Mar 20, 2024

Best Answer

+410

+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

2⁺¹ Answers

+2729

-1

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

LiIIiam0216 Mar 20, 2024

+410

+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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