How do you solve the following system?: $2 x + 3 y = 11, - x + y = - 3$ $2x+3y=11, -x+y=-3$

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Answer 1 · 2015-12-05T03:39:15

The solution for the system of equations is
$x = 4, y = 1$ $color(blue)(x=4,y=1$

$2 x + 3 y = 11$ $color(blue)(2x)+3y=11$ .....................equation $1$ $1$

$- x + y = - 3$ $-x+y = -3$ ,multiplying this equation by $2$ $2$
$- 2 x + 2 y = - 6$ $color(blue)(-2x)+2y = -6$ ..............equation $2$ $2$

Solving by elimination .

Adding equations $1$ $1$ and $2$ $2$ would result in elimination of the term $2 x$ $color(blue)(2x$ .

$cancelcolor(blue)(2x)+3y=11$
$cancelcolor(blue)(-2x)+2y = -6$

$5y=5$

$y=5/5$

$color(blue)(y=1$

Now we substitute the value of $y$ in equation $2$ to find $x$ :
$-x+y = -3$

$y +3= x$

$1 +3= x$

$color(blue)(x=4$

How do you solve the following system?: 2x+3y=11, -x+y=-3 2x+3y=11,−x+y=−3 2x+3y=11, -x+y=-3