If 5x+3y=21 and 2x−y=4, what is the value of x?
You asked:
Given the following equations: \[\begin{aligned}5 x + 3 y &= 21\\ 2 x - y &= 4\end{aligned}\] Evaluate \(x\).
MathBot Answer:
The system of linear equations has exactly one solution.
The substitution is \( x = 3 \).
\[x = 3\]
Solve \(5 x + 3 y = 21\) for \(x\). \[x = \frac{21}{5} - \frac{3 y}{5}\]
Substitute \(\frac{21}{5} - \frac{3 y}{5}\) for \(x\) in \(2 x - y = 4\) and simplify. $$\begin{aligned}2 x - y &= 4 \\ 2 \left(\frac{21}{5} - \frac{3 y}{5}\right) - y &= 4 \\ y &= 2 \end{aligned}$$
Use substitution of the numerical value of \(y\) to get the values of \(x\). $$\begin{aligned}x &= \frac{21}{5} - \frac{3 y}{5} \\ x &= \frac{21}{5} - \frac{3 \cdot 2}{5} \\ x &= 3\end{aligned}$$