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

• A. $\(\left\)(\(\frac\)12,\(\frac\)32\(\right\))$
• 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. Solve one of the equations for one variable in terms of the other. For example, from \(x + 5y = 4\), isolate \(x\): \(x = 4 - 5y\).
3. Substitute the expression for \(x\) from the second equation into the first equation: replace \(x\) in \$4x + 2y = 7\( with \)4 - 5y\( to get \)4(4 - 5y) + 2y = 7$.
4. Simplify and solve the resulting equation for \(y\): distribute 4, combine like terms, and isolate \(y\).
5. Once you find \(y\), substitute it back into \(x = 4 - 5y\) to find the corresponding value of \(x\). This gives the solution \((x, y)\) to the system.