Math Problem Solver

The system of linear equations has exactly one solution.

$$x = \frac{1000}{11}$$

$$y = \frac{100}{11}$$

Solve $x + y = 100$ for $x$. $$x = 100 - y$$

Substitute $100 - y$ for $x$ in $y = \frac{x}{10}$ and simplify. $$\begin{aligned}y &= \frac{x}{10} \\ y &= \frac{\left(100 - y\right)}{10} \\ y &= \frac{100}{11} \end{aligned}$$

Use substitution of the numerical value of $y$ to get the values of $x$. $$\begin{aligned}x &= 100 - y \\ x &= 100 - \frac{100}{11} \\ x &= \frac{1000}{11}\end{aligned}$$