Question

3x+5y=26; x+5y=22 by using Cramer's rule method​

Answer 1

Explanation:

BY CRAMER'S RULE...

in a more detailed way

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Answer 2

Given: Here we have given two equations 3x+5y=26, x+5y=22

To find: Here we have to find the values of x and y by using cramer's rule

Solution:

Here we will compare $3x+5y=26$ and $x+5y=22$ with $ax+by=c$

So,

${{a}_{1}}=5,{{b}_{1}}=5,{{c}_{1}}=26 \\ {{a}_{2}}=1,{{b}_{2}}=5,{{c}_{2}}=22$

Here we will find $D,{{D}_{x}},{{D}_{y}}$

$\begin{align} & D=\left| \begin{matrix} {{a}_{1}} & {{b}_{1}} \\ {{a}_{2}} & {{b}_{2}} \\\end{matrix} \right| \\ & =\left| \begin{matrix} 3 & 5 \\ 1 & 5 \\\end{matrix} \right| \\ & =15-5 \\ & =10 \\ \end{align}$

$& {{D}_{x}}=\left| \begin{matrix} {{c}_{1}} & {{b}_{1}} \\ {{c}_{2}} & {{b}_{2}} \\\end{matrix} \right| \\ & =\left| \begin{matrix} 26 & 5 \\ 22 & 5 \\\end{matrix} \right| \\ & =26\times 5-22\times 5 \\ & =130-110 \\ & =20$

$& {{D}_{y}}=\left| \begin{matrix} {{a}_{1}} & {{c}_{1}} \\ {{a}_{2}} & {{c}_{2}} \\\end{matrix} \right| \\ & =\left| \begin{matrix} 3 & 26 \\ 1 & 22 \\\end{matrix} \right| \\ & =22\times 3-26 \\ & =66-26 \\ & =40$

Now we will find the values of x and y

$\begin{align} & x=\frac{{{D}_{x}}}{D}=\frac{20}{10}=2 \\ & y=\frac{{{D}_{y}}}{D}=\frac{40}{10}=4 \\ & \therefore (x,y)=(2,4) \\ \end{align}$

Final answer:

Hence the answer is x=2 and y=4