Question

solve the system of equations and choose the correct ordered pair.
2x + 5y = 15
5x + 10y = 35

a. (5, 1)
b. (10, -1)
c. (10, 1)
d. (5, -1)

Explanation:

Step1: Simplify the second equation

Divide the second equation \(5x + 10y = 35\) by 5, we get \(x + 2y = 7\), then express \(x\) as \(x = 7 - 2y\).

Step2: Substitute \(x\) into the first equation

Substitute \(x = 7 - 2y\) into \(2x + 5y = 15\), we have \(2(7 - 2y) + 5y = 15\).
Expand the left side: \(14 - 4y + 5y = 15\), which simplifies to \(14 + y = 15\).

Step3: Solve for \(y\)

Subtract 14 from both sides: \(y = 15 - 14 = 1\).

Step4: Solve for \(x\)

Substitute \(y = 1\) into \(x = 7 - 2y\), we get \(x = 7 - 2\times1 = 5\).

Answer:

A. (5, 1)