Answer :
Hello
To solve this question, we are asked to use substitution method.
The given equation is
[tex]\begin{gathered} 3x+y=2\ldots\text{equ(i)} \\ y-x=-6\ldots\text{equ(}ii) \end{gathered}[/tex]From equation (ii), let's make y the subject of formula
[tex]\begin{gathered} y-x=-6 \\ y=x-6\ldots\text{equ(}iii) \end{gathered}[/tex]Put equation (iii) into equation (i)
[tex]\begin{gathered} 3x+y=2 \\ y=x-6 \\ 3x+(x-6)=2 \\ 3x+x-6=2 \\ \text{collect like terms} \\ 4x=2+6 \\ 4x=8 \\ \text{divide both sides by the coefficient of x} \\ \frac{4x}{4}=\frac{8}{4} \\ x=2 \end{gathered}[/tex]We have the value of one of the ordered pair and we can use it to find the other one.
Put x = 2 in either equation (i) or (ii)
Using equation (ii)
[tex]\begin{gathered} y-x=-6 \\ x=2 \\ y-(2)=-6 \\ \text{collect like terms} \\ y=-6+2 \\ y=-4 \end{gathered}[/tex]The value of x and y is (2, -4) and the ordered pair can be written as (2, -4)