Use substitution to solve the following system of linear equations.
$4x+2y=7$
$x+5y=4$

• A. $(\frac{1}{2},\frac{3}{2})$
• B. $\(\left\)(\(\frac\)32,\(\frac\)12\(\right\))$
• C. $\(\left\)(-\(\frac\)23,\(\frac\)13\(\right\))$
• D. $\(\left\)(-\(\frac\)13,\(\frac\)23\(\right\))$

Answer: (B)

Verified step by step guidance

1. Start with the given system of equations: \$4x + 2y = 7\( and \)x + 5y = 4$.
2. Use substitution by solving the second equation for \(x\) : \(x = 4 - 5y\).
3. Substitute \(x = 4 - 5y\) into the first equation to replace \(x\) : \$4(4 - 5y) + 2y = 7$.
4. Simplify and solve the resulting equation for \(y\) : \$16 - 20y + 2y = 7\( which simplifies to \)16 - 18y = 7$.
5. After finding \(y\) , substitute it back into \(x = 4 - 5y\) to find the value of \(x\) , giving the solution \((x, y)\) to the system.