Question

Which statement best describes the solution to this system of equations? 3x+y=17 X+2y=49

A. It has no solution.
B. It has infinite solutions.
C. It has a single solution: x= 15, y= 17.
D. It has a single solution: X=-3, y= 26.​

Answer 1

D. It has a single solution: X=-3, y= 26.

Explanation:

3x + y = 17

x + 2y = 49 ➡ x = 49 - 2y now write this information in the first equation instead of x

3x + y = 17 ➡ 3(49 - 2y) + y = 17

147 - 6y + y = 17 add like terms

147 - 17 = 5y

130 = 5y divide both sides by 5

26 = y we can calculate the value of x using this information

3x + y = 17 ➡ 3x + 26 = 17 subtract 26 from both sides

3x = -9 divide both sides by 3

x = -3