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

• A. $\left(\frac12,\frac32\right)$
• B. $\left(\frac32,\frac12\right)$
• C. $\left(-\frac23,\frac13\right)$
• D. $\left(-\frac13,\frac23\right)$

Answer: (B)

Verified step by step guidance

1. Start with the given system of equations: \[4x + 2y = 7\] \[x + 5y = 4\]
2. Use substitution by solving one of the equations for one variable. For example, solve the second equation for \(x\): \[x = 4 - 5y\]
3. Substitute the expression for \(x\) from step 2 into the first equation: \[4(4 - 5y) + 2y = 7\]
4. Simplify and solve the resulting equation for \(y\): \[16 - 20y + 2y = 7\] Combine like terms and isolate \(y\).
5. Once you find the value of \(y\), substitute it back into the expression for \(x\) from step 2 to find the value of \(x\).