Sites: Global Q&A | Wits | MathsGee Club | Joburg Libraries | StartUps | Zimbabwe | OER

MathsGee is Zero-Rated (You do not need data to access) on: Telkom |Dimension Data | Rain | MWEB

0 like 0 dislike
36 views
Solve the simultaneous equations: $\frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2$ and $\frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1$
| 36 views

0 like 0 dislike

$x = \dfrac{4}{9}$

$y = \dfrac{9}{25}$

Explanation

Let $\frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2$ be equation 1 and  $\frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1$ be equation 2.

multiply equation 1 by 2 so we can eliminate $x$

Equation 1 becomes:

$\frac{4}{\sqrt{x}}+\frac{6}{\sqrt{y}}=4$

Now subtract equation 1 from equation 2 to get:

$\frac{6}{\sqrt{y}}-\frac{9}{\sqrt{y}}=4$

$\frac{-3}{\sqrt{y}}=-5$

multiply both side by $\sqrt{y}$ to get $-3=-5\sqrt{y}$

$y = \dfrac{9}{25}$

To get $x$ we substitute $y$  in equation 1 to get:

$\frac{2}{\sqrt{x}}=2-5$

so

$\dfrac{2}{3}=\sqrt{x}$

$\therefore x = \dfrac{4}{9}$

by Diamond (88,180 points)

1 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
1 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
1 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
1 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
1 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike
0 like 0 dislike