x+y=120;
2x+y/2=150;
find value of x and y
You asked:
Given \( x + y = 120 \), \( 2 x + \frac{y}{2} = 150 \), evaluate \( x \), \( y \).
MathBot Answer:
The system of linear equations has exactly one solution.
The substitutions are \( x = 60 \), \( y = 60 \).
\[x = 60\]
\[y = 60\]
Solve \(x + y = 120\) for \(x\). \[x = 120 - y\]
Substitute \(120 - y\) for \(x\) in \(2 x + \frac{y}{2} = 150\) and simplify. $$\begin{aligned}2 x + \frac{y}{2} &= 150 \\ 2 \left(120 - y\right) + \frac{y}{2} &= 150 \\ y &= 60 \end{aligned}$$
Use substitution of the numerical value of \(y\) to get the values of \(x\). $$\begin{aligned}x &= 120 - y \\ x &= 120 - 60 \\ x &= 60\end{aligned}$$