How do solve the following linear system?: $x= y - 11 , y = 4x + 4$ ?

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Answer 1 · 2016-06-29T19:29:02

Soln. is $(x,y)=(7/3,40/3).$

Submit the value of $y,$ taken from $2^(nd)$ eqn., in the $1^(st)$ eqn. to get,

$x=4x+4-11 rArr x-4x=4-11 rArr -3x=-7 rArr x=-7/-3=7/3.$

Hence, by $2^(nd)$ eqn., $y=4(7/3)+4=28/3+4=40/3.$

Soln. is $(x,y)=(7/3,40/3).$

Answer 2 · 2016-06-29T19:30:01

$x = 7/3 = 2 1/3 and y = 40/3 = 13 1/3$

There are several methods you can use, but there is a single $y$ term in each equation, so equating them is probably the easiest method.

Change the first equation to: $y = x+11$

Now, the y in each equation is the same, so;

if: $" " y = y$
then: $" "4x + 4 = x + 11$

$" "4x - x = 11-4$
$" " 3x = 7$

$x = 7/3 = 2 1/3$

To find the value of $y$ , substitute $x = 7/3$ into either of the equations above ..... or both, to check that they give the same answer.

$y = 4xx 7/3 +4 = 40/3 " and " y = 7/3 +11 = 40/3$

How do solve the following linear system?: x= y - 11 , y = 4x + 4 x= y - 11 , y = 4x + 4 ?