Answer:
The solution to the system of equations is
(x, y) = (4, 5)
Explanation:
Given the pair of equations:
[tex]\begin{gathered} 7x-4y=8\ldots.\ldots..\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}\mathrm{}(1) \\ -2x+3y=7\ldots\ldots\ldots\ldots\ldots.\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}\mathrm{}(2) \end{gathered}[/tex]To know the solution to the system, we solve the equations simultaneously.
From equation (1), making x the subject, we have:
[tex]x=\frac{8+4y}{7}\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}(3)[/tex]Substituting equation (3) in (2)
[tex]\begin{gathered} -2(\frac{8+4y}{7})+3y=7 \\ \\ \text{Multiply both sides by 7} \\ \\ -2(8+4y)+21y=49 \\ -16-8y+21y=49 \\ -16+13y=49 \\ \\ \text{Add 16 to both sides} \\ -16+13y+16=49+16 \\ 13y=65 \\ \\ \text{Divide both sides by 13} \\ y=\frac{65}{13}=5 \end{gathered}[/tex]The value of y is 5
Using y = 5 in equation (3)
[tex]\begin{gathered} x=\frac{8+4(5)}{7} \\ \\ =\frac{8+20}{7} \\ \\ =\frac{28}{7} \\ \\ =4 \end{gathered}[/tex]The value of x is 4
