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Sagot :
Answer:
x = 3
y = 7
Explanation:
First, we need to take the first equation and solve for y as follows:
[tex]\begin{gathered} 3x-2y=-5 \\ 3x-2y-3x=-5-3x \\ -2y=-5-3x \\ \frac{-2y}{-2}=\frac{-5-3x}{-2} \\ y=2.5+1.5x \end{gathered}[/tex]Then, we can replace y with (2.5 + 1.5x) on the second equation, so:
[tex]\begin{gathered} 4x+5y=47 \\ 4x+5(2.5+1.5x)=47_{} \end{gathered}[/tex]So, solving for x, we get:
[tex]\begin{gathered} 4x+5(2.5)+5(1.5x)=47 \\ 4x+12.5+7.5x=47 \\ 11.5x+12.5=47 \\ 11.5x+12.5-12.5=47-12.5 \\ 11.5x=34.5 \\ \frac{11.5x}{11.5}=\frac{34.5}{11.5} \\ x=3 \end{gathered}[/tex]Therefore, the value of x is 3.
Finally, we can calculate the value of y as follows:
[tex]\begin{gathered} y=2.5+1.5x \\ y=2.5+1.5(3) \\ y=2.5+4.5 \\ y=7 \end{gathered}[/tex]So, the solution of the system is x = 3 and y = 7
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