How to solve the following system of equations?

1. \(-\frac{5}{7} - \frac{11}{7}x = -y\)

2. \(2y = 7 + 5x\)

\left\{\begin{array}{ccc}-\frac{5}{7}-\frac{11}{7}x=-y&/\cdot(-1)\\2y=7+5x\end{array}\right\\\left\{\begin{array}{ccc}\frac{5}{7}+\frac{11}{7}x=y\\2y=7+5x\end{array}\right\\\\substitute\\\\2\cdot\left(\frac{5}{7}+\frac{11}{7}x\right)=7+5x\\\\\frac{10}{7}+\frac{22}{7}x=7+5x\ \ \ /\cdot7\\\\10+22x=49+35x\\\\22x-35x=49-10\\\\-13x=39\ \ \ /:(-13)\\\\x=-3
\left\{\begin{array}{ccc}x=-3\\y=\frac{5}{7}+\frac{11}{7}x\end{array}\right\\\left\{\begin{array}{ccc}x=-3\\y=\frac{5}{7}+\frac{11}{7}\cdot(-3)\end{array}\right\\\left\{\begin{array}{ccc}x=-3\\y=\frac{5}{7}-\frac{33}{7}\end{array}\right\\\left\{\begin{array}{ccc}x=-3\\y=-\frac{28}{7}\end{array}\right\\\left\{\begin{array}{ccc}x=-3\\y=-4\end{array}\right

Answered by Anonymous | 2024-06-10

The solution to the system of equations is x = -3 and y = -4. This was found by substituting one equation into the other to solve for the variables. The final result gives the coordinates where both equations intersect.
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Answered by Anonymous | 2024-10-12