2x +5y-9=0 and 3x-y -5=0 solve for x and y
You asked:
Given \( 2 x + 5 y - 9 = 0 \), \( 3 x - y - 5 = 0 \), evaluate \( x \), \( y \).
MathBot Answer:
The system of linear equations has exactly one solution.
The substitutions are \( x = 2 \), \( y = 1 \).
\[x = 2\]
\[y = 1\]
Solve \(2 x + 5 y - 9 = 0\) for \(x\). \[x = \frac{9}{2} - \frac{5 y}{2}\]
Substitute \(\frac{9}{2} - \frac{5 y}{2}\) for \(x\) in \(3 x - y - 5 = 0\) and simplify. $$\begin{aligned}3 x - y - 5 &= 0 \\ 3 \left(\frac{9}{2} - \frac{5 y}{2}\right) - y - 5 &= 0 \\ y &= 1 \end{aligned}$$
Use substitution of the numerical value of \(y\) to get the values of \(x\). $$\begin{aligned}x &= \frac{9}{2} - \frac{5 y}{2} \\ x &= \frac{9}{2} - \frac{5 \cdot 1}{2} \\ x &= 2\end{aligned}$$