Solve for ‘x’ and ‘y’ find the ordered pair (x,y)
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Answer: For [tex]3x+2y=8,[/tex] we have [tex](0,4), (2,1)[/tex] and for [tex]x/3+x/2=4[/tex] we have [tex](12,0),(0,8).[/tex]
Explanation:
(a) Given that [tex]3x+2y=8[/tex]
To find the ordered pair [tex](x,y)[/tex], we start by subsituting the value of [tex]x=0.[/tex]
⇒[tex]3x+2y=8[/tex],
⇒[tex]2y=8[/tex],
⇒[tex]y=4[/tex].
So first ordered pair is [tex](0,4).[/tex]
Similarly, putting value of [tex]x=2[/tex], we get:
⇒[tex]3(2)+2y=8[/tex],
⇒[tex]6+2y=8[/tex],
⇒[tex]2y=8-6=2[/tex],
⇒[tex]y=1.[/tex]
Secon,ordered pair is [tex](2,1).[/tex]
(b) Given the next equation [tex]x/3+y/2=4.[/tex]
On simplifying, [tex]2x+3y=6*4[/tex]
⇒[tex]2x+3y=24,[/tex]
For ordered pair, we put [tex]x=0[/tex] , we get [tex]y=24/3=8[/tex]
So we get [tex](0,8)[/tex].
Similary, putting [tex]y=0[/tex], we get [tex]x=24/2=12.[/tex]
Therefore, we have [tex](12,0)[/tex] as the ordered pair.
Question:
Solve for ‘x’ and ‘y’ and find the ordered pair (x,y).
3x + 2y = 8
( x / 3 ) + ( y / 2 ) = 4
Answer:
The solution of the given equations is
( x, y ) = ( 24 / 5, 56 / 5 ).
Step-by-step-explanation:
The given linear equations are
3x + 2y = 8 - - - ( 1 )
( x / 3 ) + ( y / 2 ) = 4
⇒ ( 2x + 3y ) / 6 = 4
⇒ 2x + 3y = 24
⇒ 2x = 24 - 3y
⇒ x = ( 24 - 3y ) / 2 - - - ( 2 )
By substituting equation ( 2 ) in equation ( 1 ), we get,
3x + 2y = 8 - - - ( 1 )
⇒ [ 3 * ( 24 - 3y ) / 2 ] + 2y = 8
⇒ [ ( 72 - 9y ) / 2 ] + 2y = 8
⇒ ( 72 - 9y + 4y ) / 2 = 8
⇒ 72 - 5y = 8 * 2
⇒ - 5y + 72 = 16
⇒ - 5y = 16 - 72
⇒ - 5y = - 56
⇒ 5y = 56
⇒ y = 56 / 5
By substituting this value in equation ( 2 ),
x = ( 24 - 3y ) / 2 - - - ( 2 )
⇒ x = ( 24 - 3 * 56 / 5 ) / 2
⇒ x = [ 24 - ( 168 / 5 ) ] / 2
⇒ x = [ ( 120 - 168 ) / 5 ] / 2
⇒ x = ( 48 / 5 ) / 2
⇒ x = 48 / 5 * 1 / 2
⇒ x = 48 / 10
⇒ x = 24 / 5
∴ The solution of the given equations is
( x, y ) = ( 24 / 5, 56 / 5 ).