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Sagot :
We are given two equations involving x and y
[tex]\begin{gathered} 8x+3y=-4\text{ eq. 1} \\ 5x+2y=6\text{ eq. 2} \end{gathered}[/tex]We want to solve these equations and find out the values of x and y.
We can use the substitution method to solve these equations.
[tex]\begin{gathered} 5x+2y=6 \\ 2y=6-5x \\ y=\frac{6-5x}{2}\text{ eq. 3} \end{gathered}[/tex]Substitute eq. 3 into eq. 1 and then simplify.
[tex]\begin{gathered} 8x+3y=-4 \\ 8x+3(\frac{6-5x}{2})=-4 \\ 8x+\frac{18-15x}{2}=-4 \\ \frac{2(8x)+18-15x}{2}=-4 \\ 16x+18-15x=-8 \\ 16x-15x=-8-18 \\ x=-26 \end{gathered}[/tex]So we have found the value of x.
Now substitute the value of x into eq. 3 to get the value of y.
[tex]\begin{gathered} y=\frac{6-5x}{2} \\ y=\frac{6-5(-26)}{2} \\ y=\frac{6+130}{2} \\ y=\frac{136}{2} \\ y=68 \end{gathered}[/tex]So we have found the value of y.
Therefore, the solution is
[tex]\begin{gathered} x=-26 \\ y=68 \end{gathered}[/tex]
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