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Sagot :
Answer: x=-6 and y=-2
Given:
[tex]\begin{gathered} x=y-4 \\ -2x+3y=6 \end{gathered}[/tex]Having these two equations, we can substitute the first equation with the second equation to solve for y:
[tex]\begin{gathered} -2x+3y=6 \\ \end{gathered}[/tex]Since the first equation says that x = y - 4,
[tex]\begin{gathered} -2x+3y=6 \\ -2(y-4)+3y=6 \\ -2y+8+3y=6 \\ -2y+3y=6-8 \\ y=-2 \end{gathered}[/tex]Then, we will substitute this y-value to the first equation to solve for x.
[tex]\begin{gathered} x=y-4 \\ x=-2-4 \\ x=-6 \end{gathered}[/tex]We now have the values x=-6 and y=-2. To check, let us substitute both values to the second equation
[tex]\begin{gathered} -2x+3y=6 \\ -2(-6)+3(-2)=6 \\ 12-6=6 \\ 6=6 \end{gathered}[/tex]Therefore, the answer is correct, and the answer is x=-6 and y=-2
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