2x + 3y = 5
4x - y = 9
find x and y
You asked:
Given \( 2 x + 3 y = 5 \), \( 4 x - y = 9 \), evaluate \( x \), \( y \).
MathBot Answer:
The system of linear equations has exactly one solution.
The substitutions are \( x = \frac{16}{7} \), \( y = \frac{1}{7} \).
\[x = \frac{16}{7}\]
\[y = \frac{1}{7}\]
Solve \(2 x + 3 y = 5\) for \(x\). \[x = \frac{5}{2} - \frac{3 y}{2}\]
Substitute \(\frac{5}{2} - \frac{3 y}{2}\) for \(x\) in \(4 x - y = 9\) and simplify. $$\begin{aligned}4 x - y &= 9 \\ 4 \left(\frac{5}{2} - \frac{3 y}{2}\right) - y &= 9 \\ y &= \frac{1}{7} \end{aligned}$$
Use substitution of the numerical value of \(y\) to get the values of \(x\). $$\begin{aligned}x &= \frac{5}{2} - \frac{3 y}{2} \\ x &= \frac{5}{2} - \frac{3 \cdot \frac{1}{7}}{2} \\ x &= \frac{16}{7}\end{aligned}$$