what is the solution to the system of equations below?\n$2x + 3y = 17$\n$3x + 6y = 30$\n$\\circ\\ (-7…

what is the solution to the system of equations below?\n$2x + 3y = 17$\n$3x + 6y = 30$\n$\\circ\\ (-7, 24)$\n$\\circ\\ (3, 4)$\n$\\circ\\ (4, 3)$\n$\\circ\\ (24, -7)$

what is the solution to the system of equations below?\n$2x + 3y = 17$\n$3x + 6y = 30$\n$\\circ\\ (-7, 24)$\n$\\circ\\ (3, 4)$\n$\\circ\\ (4, 3)$\n$\\circ\\ (24, -7)$

Answer

Explanation:

Step1: Simplify the second equation

Divide the second equation (3x + 6y = 30) by 3, we get (x + 2y = 10), and then express (x) as (x = 10 - 2y).

Step2: Substitute into the first equation

Substitute (x = 10 - 2y) into the first equation (2x + 3y = 17): [ \begin{align*} 2(10 - 2y) + 3y &= 17\ 20 - 4y + 3y &= 17\ 20 - y &= 17\ -y &= 17 - 20\ -y &= -3\ y &= 3 \end{align*} ]

Step3: Find the value of (x)

Substitute (y = 3) into (x = 10 - 2y), we get (x = 10 - 2\times3 = 10 - 6 = 4).

Answer:

((4, 3))