![\[\mathbf{x}\text{ }+\text{ }\mathbf{2y}\text{ }+\text{ }\mathbf{1}\text{ }=\text{ }\mathbf{0}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e3de616fd05cec3f1455c5451d8c5f41_l3.png "Rendered by QuickLaTeX.com")
![\[\mathbf{2x}\text{ }\text{ }\mathbf{3y}\text{ }\text{ }\mathbf{12}\text{ }=\text{ }\mathbf{0}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-4eeffcfaa10c1fd058684a58edd686fc_l3.png "Rendered by QuickLaTeX.com")
![\[\mathbf{3x}\text{ }+\text{ }\mathbf{2y}\text{ }+\text{ }\mathbf{25}\text{ }=\text{ }\mathbf{0}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6a9d123021bd390428c8ec7e71c15e0c_l3.png "Rendered by QuickLaTeX.com")
![\[\mathbf{2x}\text{ }+\text{ }\mathbf{y}\text{ }+\text{ }\mathbf{10}\text{ }=\text{ }\mathbf{0}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3eb17086666e9dc022d5282d63492807_l3.png "Rendered by QuickLaTeX.com")
Solution:
Given
Cross multiplication Method
![\[\frac{x}{{{b}_{1}}{{c}_{2}}-{{b}_{2}}{{c}_{1}}}=\frac{-y}{{{a}_{1}}{{c}_{2}}-{{a}_{2}}{{c}_{1}}}=\frac{1}{{{a}_{1}}{{b}_{2}}-{{a}_{2}}{{b}_{1}}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-007fa7175ae1f5c3950c34825b73ca25_l3.png "Rendered by QuickLaTeX.com")
![\[{{a}_{1}}=1,{{b}_{1}}=2,{{c}_{1}}=1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ed865e3262e04ed8012e2b152b77948c_l3.png "Rendered by QuickLaTeX.com")
![\[{{a}_{2}}=2,{{b}_{2}}=3,{{c}_{2}}=12\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e5218a796ca09b2e202640411d34d268_l3.png "Rendered by QuickLaTeX.com")
Calculation,
![\[\frac{x}{-21}=\frac{-y}{-14}=\frac{1}{-7}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8fc4191780cdd3648d49229f58a75fbd_l3.png "Rendered by QuickLaTeX.com")
= 
And,
= 
Solution:
Given
By cross multiplication method
Comparing the two equations
![\[{{a}_{1}}=3,{{b}_{1}}=2,{{c}_{1}}=25\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d7d76e9c2521920e35d8a9760a9e6bd6_l3.png "Rendered by QuickLaTeX.com")
![\[{{a}_{2}}=2,{{b}_{2}}=3,{{c}_{2}}=10\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c4b01c03038b25b56790da296521e62e_l3.png "Rendered by QuickLaTeX.com")
Calculation
![\[\frac{x}{-5}=\frac{-y}{-20}=\frac{1}{-1}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-99b8052e2a6388b2952fd9053eb60c69_l3.png "Rendered by QuickLaTeX.com")
= 
And,
= 
Solution:
Given
Cross multiplication Method
Calculation,
=
And,
=
Solution:
Given
By cross multiplication method
Comparing the two equations
Calculation
=
And,
=