Question

15 Solve the equations by substitution method
√2x+√3y=0
√3x - √8y=0​

Answer 1

$\LARGE{\underline{\bf{Required\: Answer :}}}$

We have,

• √2x + √3y = 0
• √3x - √8y = 0

From Equation (1), We deduce:

⇒ √2x = -√3y

⇒ x = -√3y / √2

Plugging in equation (2),

⇒ √3(-√3y/√2) - √8y = 0

⇒ -3y/√2 - 2√2y = 0

Taking y in common,

⇒ y ( -3/√2 - 2√2) = 0

⇒ y = 0

Then,

⇒ x = -√3 × 0 / √2

⇒ x = 0

Hence,

The required value of x and y:

$\huge{ \boxed{ \red{ \sf{0 \:and \: 0}}}}$

Explore more!!

For solving the above, you can also try using the other ways of solving like:

• Graphical method
• Elimination method
• Cross multiplication method.

Answer 2

Answer:

Given:

√2x+√3y=0

√3x-√8y=0

To find:

solve by substitution method.

Solution:

Let,

Solve equation (a) and put the value in the equation (b):

$\begin{gathered}\to \sqrt{2}x+\sqrt{3}y=0\\\\\to \sqrt{2}x=-\sqrt{3}y\\\\\to x=-\frac{\sqrt{3} y}{\sqrt{2}}\\\\\to x=-\frac{\sqrt{3} y}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}\\\\\to x=-\frac{\sqrt{3}\sqrt{2} y}{2} \\\\\to x=-\frac{\sqrt{6} y}{2} \\\\\end{gathered}$

equation (b):

$\begin{gathered}\to \sqrt{3}x-\sqrt{8}y=0\\\\\end{ggathered$

$\begin{gathered}\to \sqrt{3}(-\frac{\sqrt{6}y}{{2}})-\sqrt{8}y=0\\\\\to - \sqrt{3}(\frac{\sqrt{3} \times \sqrt{2} y}{{2}})-\sqrt{8}y=0\\\\\to -\frac{3 \sqrt{2} y}{{2}}-2\sqrt{2}y=0\\\\\to \frac{-3 \sqrt{2}y-4\sqrt{2}y}{2}=0\\\\\to \frac{-3 \sqrt{2}y-4\sqrt{2}y}{2}=0\\\\\to -\sqrt{2}y(\frac{3+4}{2})=0\\\\\to -\sqrt{2}y(\frac{7}{2})=0\\\\\to y= - \frac{2}{7\sqrt{2}}\\\\\to y= - \frac{2}{7\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}\\\\\to y= - \frac{2\sqrt{2}}{7\times 2} \\\\\to y= - \frac{\sqrt{2}}{7} \\\\\end{ggathered$

put the value of y into the equation (a):

Equation (a):

$\to \sqrt{2}x+\sqrt{3}$

$\begin{gathered}\to \sqrt{2}x+\sqrt{3} \times (-\frac{\sqrt{2}}{7})=0\\\\\to \sqrt{2}x- \frac{\sqrt{2}\sqrt{3}}{7}=0\\\\\to \sqrt{2}x- \frac{\sqrt{3}\sqrt{2}}{7}=0\\\\\to \sqrt{2}x = \frac{\sqrt{3}\sqrt{2}}{7}\\\\\to x = \frac{\sqrt{3}\sqrt{2}}{7 \sqrt{2}}\\\\\to x = \frac{\sqrt{3}}{7}\\\\\end{gathered}$

$The \:final \:value \:of \:x \:and \:y\: is: \begin{gathered}\bold{-\frac{\sqrt{2}}{7} \ \ _{and} \ \ \frac{\sqrt{3}}{7}}\\\end{gathered}$