Answer
The solution is $(2,1)$.
Work Step by Step
The given system of equations is
$x+y=3$ ...... (1)
$x+2y=4$ ...... (2)
Multiply equation (1) by $-1$.
$-1(x+y)=-1(3)$
Use distributive property.
$-x-y=-3$ ...... (3)
Add equation (2) and (3).
$\Rightarrow x+2y-x-y=4-3$
Add like terms.
$\Rightarrow y=1$
Substitute $1$ for $y$ in equation (1).
$\Rightarrow x+1=3$
Subtract $1$ from each side.
$\Rightarrow x+1-1=3-1$
Simplify.
$\Rightarrow x=2$
Check $(x,y)=(2,1)$
Equation (1):
$\Rightarrow x+y=3$
$\Rightarrow 2+1=3$
$\Rightarrow 3=3$
True.
Equation (2):
$\Rightarrow x+2y=4$
$\Rightarrow 2+2(1)=4$
$\Rightarrow 2+2=4$
$\Rightarrow 4=4$
True.
Hence, the solution is $(2,1)$.
