[tex]\bold{\huge{\pink{\underline{ Solution }}}}[/tex]
[tex]\bold{\underline{ Given }}[/tex]
- We have given two linear equations that is 2x - 3y = -6 and x + 3y = 12 .
[tex]\bold{\underline{ To \: Find }}[/tex]
- We have to find the value of x and y by elimination method.
[tex]\bold{\underline{ Let's \: Begin }}[/tex]
[tex]\sf{ 2x - 3y = -6 ...eq(1)}[/tex]
[tex]\sf{ x + 3y = 12 ...eq(2)}[/tex]
Multiply eq( 2 ) by 2 :-
[tex]\sf{ 2( x + 3y = 12 )}[/tex]
[tex]\sf{ 2x + 6y = 24 }[/tex]
Subtract eq(1) from eq(2) :-
[tex]\sf{ 2x + 6y -( 2x - 3y) = 24 -(-6)}[/tex]
[tex]\sf{ 2x + 6y - 2x + 3y = 24 + 6 }[/tex]
[tex]\sf{ 9y = 30 }[/tex]
[tex]\sf{ y = 30/9}[/tex]
[tex]\sf{\red{ y = 10/3}}[/tex]
Now, Subsitute the value of y in eq( 1 ):-
[tex]\sf{ 2x - 3(10/3) = -6 }[/tex]
[tex]\sf{ 2x - 10 = -6 }[/tex]
[tex]\sf{ 2x = -6 + 10}[/tex]
[tex]\sf{ x = 4/2}[/tex]
[tex]\sf{\red{ x = 2}}[/tex]
Hence, The value of x and y is 2 and 10/3
