y = 2x - 7
y = $\sqrt{-2x + 9}$
You asked:
Solve the system of equations:\[\begin{aligned}y &= 2 x - 7\\y &= \sqrt{-\left( 2 x \right) + 9}\end{aligned}\]
MathBot Answer:
The system of equations has one solution.
\[x = 4, y = 1\]
Solve \(y = 2 x - 7\) for \(x\). \[x = \frac{y}{2} + \frac{7}{2}\]Substitute \(\frac{y}{2} + \frac{7}{2}\) for \(x\) in \(y = \sqrt{9 - 2 x}\) and simplify. $$\begin{aligned}y &= \sqrt{9 - 2 x} \\ y &= \sqrt{9 - 2 \left(\frac{y}{2} + \frac{7}{2}\right)} \\ y &= \sqrt{2 - y} \end{aligned}$$Substitute \(1\) into \(y = 2 x - 7\) to solve for \(x\). \[\begin{aligned}1 &= 2 x - 7\\- 2 x &= -8\\x &= 4\end{aligned}\]This yields the following solution. $$\begin{aligned}x = 4,\,y = 1\end{aligned}$$