Let us write out the equation,
[tex]\begin{gathered} 3x+y=6\ldots\ldots\text{.}.1 \\ y=-4x+5\ldots\ldots2 \end{gathered}[/tex]We will apply the method of substitution to resolve the equations.
Let us make y the subject of the formula in equation 1,
[tex]\begin{gathered} 3x+y=6 \\ y=6-3x\ldots\ldots\ldots.3 \end{gathered}[/tex]Let us substitute the value of y=6-3x into equation 2, and solve for x
[tex]\begin{gathered} 6-3x=-4x+5 \\ \text{collect like terms} \\ -3x+4x=5-6 \\ x=-1 \end{gathered}[/tex]Let us solve for y by substituting the value of x= -1 into equation 3.
[tex]\begin{gathered} y=6-3x \\ y=6-3(-1) \\ y=6+3 \\ y=9 \end{gathered}[/tex]Hence, the solution of the equation is (x,y)= (-1,9).
The correct option is option 1.
