How do you solve the following linear system: $4x + 5y = -3 , -x + y = 3$ ?

Question

Replaced a $+$ with $=$ for the first equation; hopefully, this is what was intended.

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Answer 1 · 2015-11-13T13:19:09

$x=-2$ , $y=-1$ .

From the second equation, we know that $y=3+x$ .

So, the first equation becomes

$4x+5color(green)(y)=-3 -> 4x+5color(green)((3+x))=-3$

Expand the left memeber: $4x+15+5x = 9x+15$

So, $9x+15=-3 \iff 9x = -18 iff x=-2$

Knowing this, we obtain $y$ , since $y=3+x=3-2=1$

Answer 2 · 2015-11-13T13:20:23

$(x,y)=(-2,1)$

Given
[1] $color(white)("XXX")4x+5y=-3$
[2] $color(white)("XXX")-x+y=3$

Multiply [2] by $4$
[3] $color(white)("XXX")-4x+4y=12$

Add [1] and [3]
[4] $color(white)("XXX")9y=9$

Divide [4] by $9$
[5] $color(white)("XXX")y=1$

Substitute $1$ for $y$ in [2]
[6] $color(white)("XXX")-x+(1)=3$

Subtract $1$ from both sides of [6]
[7] $color(white)("XXX")-x=2$

Multiply both sides of [7] by $(-1)$
[8] $color(white)("XXX")x=-2$