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Sagot :
The first system of equations is
[tex]\mleft\{\begin{aligned}5x+6y=-9 \\ 7x+2y=13\end{aligned}\mright.[/tex]To solve this system, we multiply the second equation by -3, that way we'll be able to eliminate y and solve for x.
[tex]\begin{gathered} \mleft\{\begin{aligned}5x+6y=-9 \\ -21x-6y=-39\end{aligned}\mright. \\ 5x-21x+6y-6y=-9-39 \\ -16x=-48 \\ x=\frac{-48}{-16}=3 \end{gathered}[/tex]Then, we use the value of x to find y.
[tex]\begin{gathered} 5x+6y=-9 \\ 5(3)+6y=-9 \\ 15+6y=-9 \\ 6y=-9-15 \\ 6y=-24 \\ y=\frac{-24}{6} \\ y=-4 \end{gathered}[/tex]Therefore, the solutions are x = 3 and y = -4.
The second system of linear equations is
[tex]\mleft\{\begin{aligned}2x-9y=-10 \\ 3x+5y=22\end{aligned}\mright.[/tex]To solve this system, we multiply the first equation by -3/2.
[tex]\begin{gathered} \mleft\{\begin{aligned}-3x+\frac{27}{2}y=15 \\ 3x+5y=22\end{aligned}\mright. \\ -3x+3x+\frac{27}{2}y+5y=15+22 \\ \frac{27y+10y}{2}=37 \\ \frac{37y}{2}=37 \\ y=\frac{37\cdot2}{37} \\ y=2 \end{gathered}[/tex]Then, we use this value to find x.
[tex]\begin{gathered} 2x-9y=-10 \\ 2x-9(2)=-10 \\ 2x-18=-10 \\ 2x=18-10 \\ 2x=8 \\ x=\frac{8}{2} \\ x=4 \end{gathered}[/tex]Therefore, the solutions are x = 4 and y = 2.
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