x+2y=8 and 3x+2y=12 find x and y
You asked:
Given \( x + 2 y = 8 \), \( 3 x + 2 y = 12 \), evaluate \( x \), \( y \).
MathBot Answer:
The system of linear equations has exactly one solution.
\[x = 2\]
\[y = 3\]
Solve \(x + 2 y = 8\) for \(x\). \[x = 8 - 2 y\]
Substitute \(8 - 2 y\) for \(x\) in \(3 x + 2 y = 12\) and simplify. $$\begin{aligned}3 x + 2 y &= 12 \\ 3 \left(8 - 2 y\right) + 2 y &= 12 \\ y &= 3 \end{aligned}$$
Use substitution of the numerical value of \(y\) to get the values of \(x\). $$\begin{aligned}x &= 8 - 2 y \\ x &= 8 - 2 \cdot 3 \\ x &= 2\end{aligned}$$