Question

8. What is the solution point for the system 2x - 3y = 4 & y=-4X - 6? *O (5.-2)(-2,5)O (-1,-2)O (-2,-1)

Answer 1

A system of two equations with two unknowns is given:

`\begin{gathered} 2x-3y=4 \\ y=-4x-6 \end{gathered}`

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:

`\begin{gathered} 2x-3y=4 \\ \Rightarrow2x-3(-4x-6)=4 \end{gathered}`

This way, we have obtained a single equation with one unknown that we can solve as usual. Solve for x:

`\begin{gathered} \Rightarrow2x+12x+18=4 \\ \Rightarrow14x=4-18 \\ \Rightarrow14x=-14 \\ \Rightarrow x=(-14)/(14) \\ \therefore x=-1 \end{gathered}`

Replace x=-1 into the equation for y to find its value:

`\begin{gathered} y=-4x-6 \\ \Rightarrow y=-4(-1)-6 \\ \Rightarrow y=4-6 \\ \therefore y=-2 \end{gathered}`

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:

`(-1,-2)`