6x+9y=21
18x+6y=84
solve for x and y
You asked:
Given \( 6 x + 9 y = 21 \), \( 18 x + 6 y = 84 \), evaluate \( x \), \( y \).
MathBot Answer:
The system of linear equations has exactly one solution.
\[x = 5\]
\[y = -1\]
Solve \(6 x + 9 y = 21\) for \(x\). \[x = \frac{7}{2} - \frac{3 y}{2}\]
Substitute \(\frac{7}{2} - \frac{3 y}{2}\) for \(x\) in \(18 x + 6 y = 84\) and simplify. $$\begin{aligned}18 x + 6 y &= 84 \\ 18 \left(\frac{7}{2} - \frac{3 y}{2}\right) + 6 y &= 84 \\ y &= -1 \end{aligned}$$
Use substitution of the numerical value of \(y\) to get the values of \(x\). $$\begin{aligned}x &= \frac{7}{2} - \frac{3 y}{2} \\ x &= - \frac{\left(-1\right) 3}{2} + \frac{7}{2} \\ x &= 5\end{aligned}$$