4x-5y=5
2x-3y=2
find x and y
You asked:
Given \( 4 x - 5 y = 5 \), \( 2 x - 3 y = 2 \), evaluate \( x \), \( y \).
MathBot Answer:
The system of linear equations has exactly one solution.
\[x = \frac{5}{2}\]
\[y = 1\]
Solve \(4 x - 5 y = 5\) for \(x\). \[x = \frac{5 y}{4} + \frac{5}{4}\]
Substitute \(\frac{5 y}{4} + \frac{5}{4}\) for \(x\) in \(2 x - 3 y = 2\) and simplify. $$\begin{aligned}2 x - 3 y &= 2 \\ 2 \left(\frac{5 y}{4} + \frac{5}{4}\right) - 3 y &= 2 \\ y &= 1 \end{aligned}$$
Use substitution of the numerical value of \(y\) to get the values of \(x\). $$\begin{aligned}x &= \frac{5 y}{4} + \frac{5}{4} \\ x &= 5 \cdot 1 \cdot \frac{1}{4} + \frac{5}{4} \\ x &= \frac{5}{2}\end{aligned}$$