We are given the following system of equations:
[tex]\begin{gathered} x+y=2,(1) \\ y=2x+5,(2) \end{gathered}[/tex]To solve this system we will use the method of substitution. We will replace the value of "y" from equation (2) into equation (1).
[tex]x+2x+5=2[/tex]Now we will add like terms:
[tex]3x+5=2[/tex]Now we will subtract 5 to both sides of the equation:
[tex]\begin{gathered} 3x+5-5=2-5 \\ 3x=-3 \end{gathered}[/tex]Now we will divide by 3:
[tex]x=-\frac{3}{3}=-1[/tex]Now we will replace the value of "x" in equation (2):
[tex]y=2(-1)+5[/tex]Solving the operations:
[tex]\begin{gathered} y=-2+5 \\ y=3 \end{gathered}[/tex]The solution of the system is:
[tex](x,y)=(-1,3)[/tex]