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 by identifying the two equations in the system: 4x + 2y = 7 and x + 5y = 4.
2. Choose one of the equations to solve for one variable in terms of the other. Let's solve the second equation, x + 5y = 4, for x. Subtract 5y from both sides to get 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, resulting in 4(4 - 5y) + 2y = 7.
4. Simplify the equation from the previous step. Distribute the 4 to get 16 - 20y + 2y = 7. Combine like terms to simplify further: 16 - 18y = 7.
5. Solve for y by isolating it on one side of the equation. Subtract 16 from both sides to get -18y = 7 - 16, which simplifies to -18y = -9. Divide both sides by -18 to find the value of y.