Math Problem Solver

The system of linear equations has exactly one solution.

The substitutions are \( x = - \frac{168}{53} \), \( y = \frac{30}{53} \).

\[x = - \frac{168}{53}\]

\[y = \frac{30}{53}\]

Solve \(- 11 x + 2 y = 36\) for \(x\). \[x = \frac{2 y}{11} - \frac{36}{11}\]

Substitute \(\frac{2 y}{11} - \frac{36}{11}\) for \(x\) in \(20 x - 47 y = -90\) and simplify. $$\begin{aligned}20 x - 47 y &= -90 \\ 20 \left(\frac{2 y}{11} - \frac{36}{11}\right) - 47 y &= -90 \\ y &= \frac{30}{53} \end{aligned}$$

Use substitution of the numerical value of \(y\) to get the values of \(x\). $$\begin{aligned}x &= \frac{2 y}{11} - \frac{36}{11} \\ x &= \frac{2 \cdot \frac{30}{53}}{11} - \frac{36}{11} \\ x &= - \frac{168}{53}\end{aligned}$$