Question

solve the system of equations and choose the correct ordered pair.
3x + 5y = 2
9x + 11y = 14
a. (3, -2)
b. (4, -2)
c. (4, 2)
d. (3, 2)

Explanation:

Step1: Multiply the first equation by 3

We have the system:
\[

$$\begin{cases} 3x + 5y = 2 \quad (1)\\ 9x + 11y = 14 \quad (2) \end{cases}$$

\]
Multiply equation (1) by 3: \(3(3x + 5y)=3\times2\), which simplifies to \(9x + 15y = 6\quad(3)\)

Step2: Subtract equation (2) from equation (3)

Subtract \((2)\) from \((3)\): \((9x + 15y)-(9x + 11y)=6 - 14\)
Simplify the left - hand side: \(9x+15y - 9x - 11y = 4y\)
Simplify the right - hand side: \(6-14=-8\)
So we get \(4y=-8\)

Step3: Solve for y

Divide both sides of \(4y = - 8\) by 4: \(y=\frac{-8}{4}=-2\)

Step4: Substitute y = - 2 into equation (1)

Substitute \(y=-2\) into \(3x + 5y = 2\): \(3x+5\times(-2)=2\)
Simplify: \(3x-10 = 2\)
Add 10 to both sides: \(3x=2 + 10=12\)
Divide both sides by 3: \(x=\frac{12}{3}=4\)

Answer:

B. \((4,-2)\)