Question

question 1 of 25
use the substitution method to solve the system of equations. choose the correct ordered pair.
$2y + 4x = 18$
$2y - 3x = 4$
a. $(6, -3)$
b. $(2, 5)$
c. $(5, -1)$
d. $(3, 3)$

Explanation:

Step1: Solve for 2y from second equation

From \(2y - 3x = 4\), we get \(2y = 3x + 4\).

Step2: Substitute 2y into first equation

Substitute \(2y = 3x + 4\) into \(2y + 4x = 18\), we have \((3x + 4)+4x = 18\).
Simplify: \(3x + 4+4x = 18\) → \(7x + 4 = 18\).
Subtract 4: \(7x = 18 - 4 = 14\).
Divide by 7: \(x=\frac{14}{7}=2\).

Step3: Find y using x = 2

Substitute \(x = 2\) into \(2y = 3x + 4\), we get \(2y = 3\times2 + 4 = 6 + 4 = 10\).
Divide by 2: \(y=\frac{10}{2}=5\).

Answer:

B. (2, 5)