Question

$$\left. \begin{array} { l } { 2 x + \frac { 5 } { 3 } = \frac { 26 } { 3 } - x } \\ { 5 x + \frac { 7 } { 2 } = \frac { 3 x } { 2 } - 14 } \end{array} \right.$$

Answer

x=0.086400604248047

Solution


Simplify  \(x\times 73x\times 145x+\)  to  \(10585{x}^{3}\).
\[2x+\frac{5}{3}=\frac{26}{3}-x\times 73x\times 145x+\]
Simplify  \(x\times 73x\times 145x+\)  to  \(10585{x}^{3}\).
\[2x+\frac{5}{3}=\frac{26}{3}-x\times 73x\times 145x+\]
Subtract \(2x\) from both sides.
\[\frac{5}{3}=\frac{26}{3}-x\times 73x\times 145x-2x\]
Take out the constants.
\[\frac{5}{3}=\frac{26}{3}-(73\times 145)xxx-2x\]
Simplify  \(73\times 145\)  to  \(10585\).
\[\frac{5}{3}=\frac{26}{3}-10585xxx-2x\]
Simplify  \(10585xxx\)  to  \(10585{x}^{3}\).
\[\frac{5}{3}=\frac{26}{3}-10585{x}^{3}-2x\]
Subtract \(\frac{26}{3}\) from both sides.
\[\frac{5}{3}-\frac{26}{3}=-10585{x}^{3}-2x\]
Simplify  \(\frac{5}{3}-\frac{26}{3}\)  to  \(-7\).
\[-7=-10585{x}^{3}-2x\]
Move all terms to one side.
\[7-10585{x}^{3}-2x=0\]
No root was found algebraically. However, the following root(s) were found by numerical methods.
\[x=0.086401\]