y=18x-30 and y=-6x+5
find x
You asked:
Solve the equations \[\begin{aligned}y &= 18 x - 30\\y &= -\left( 6 x \right) + 5\end{aligned}\] for the unknown \(x\).
MathBot Answer:
The system of linear equations has exactly one solution.
\[x = \frac{35}{24}\]
Solve \(y = 18 x - 30\) for \(x\). \[x = \frac{y}{18} + \frac{5}{3}\]
Substitute \(\frac{y}{18} + \frac{5}{3}\) for \(x\) in \(y = 5 - 6 x\) and simplify. $$\begin{aligned}y &= 5 - 6 x \\ y &= 5 - 6 \left(\frac{y}{18} + \frac{5}{3}\right) \\ y &= - \frac{15}{4} \end{aligned}$$
Use substitution of the numerical value of \(y\) to get the values of \(x\). $$\begin{aligned}x &= \frac{y}{18} + \frac{5}{3} \\ x &= - \frac{15}{4 \cdot 18} + \frac{5}{3} \\ x &= \frac{35}{24}\end{aligned}$$