solve the following simultaneous equations:

6(2x-1+y)+5=-13

y(3x+5)=3x(+y)-26

asked by guest
on Nov 24, 2024 at 3:42 pm



You asked:

Solve the system of equations:\[\begin{aligned}6 \cdot \left(2 x - 1 + y\right) + 5 &= -13\\y\left( 3 x + 5 \right) &= 3 \cdot x\left( y \right) - 26\end{aligned}\]

MathBot Answer:

The system of equations has one solution.

\[x = \frac{8}{5}, y = - \frac{26}{5}\]

Solve \(12 x + 6 y - 1 = -13\) for \(x\). \[x = - \frac{y}{2} - 1\]Substitute \(- \frac{y}{2} - 1\) for \(x\) in \(y \left(3 x + 5\right) = 3 x y - 26\) and simplify. $$\begin{aligned}y \left(3 x + 5\right) &amp= 3 x y - 26 \\ y \left(3 \left(- \frac{y}{2} - 1\right) + 5\right) &= 3 \left(- \frac{y}{2} - 1\right) y - 26 \\ y &= - \frac{26}{5} \end{aligned}$$Substitute \(- \frac{26}{5}\) into \(12 x + 6 y - 1 = -13\) to solve for \(x\). \[\begin{aligned}12 x - \frac{161}{5} &= -13\\12 x &= \frac{96}{5}\\x &= \frac{8}{5}\end{aligned}\]This yields the following solution. $$\begin{aligned}x = \frac{8}{5},\,y = - \frac{26}{5}\end{aligned}$$

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