A system of two equations with two unknowns is given:
[tex]\begin{gathered} 2x-3y=4 \\ y=-4x-6 \end{gathered}[/tex]
Notice that the variable y is isolated in the second equation. Then. we can solve the system using the substitution method by replacing y in the first equation by the expression from the second equation:
[tex]\begin{gathered} 2x-3y=4 \\ \Rightarrow2x-3(-4x-6)=4 \end{gathered}[/tex]
This way, we have obtained a single equation with one unknown that we can solve as usual. Solve for x:
[tex]\begin{gathered} \Rightarrow2x+12x+18=4 \\ \Rightarrow14x=4-18 \\ \Rightarrow14x=-14 \\ \Rightarrow x=\frac{-14}{14} \\ \therefore x=-1 \end{gathered}[/tex]
Replace x=-1 into the equation for y to find its value:
[tex]\begin{gathered} y=-4x-6 \\ \Rightarrow y=-4(-1)-6 \\ \Rightarrow y=4-6 \\ \therefore y=-2 \end{gathered}[/tex]
Then, the solution to the system is x=-1 and y=-2. As an ordered pair (x,y), the solution point for the given system is:
[tex](-1,-2)[/tex]
