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