Which of these correctly explains the solution of the system of equations shown below?
2 x + 3 y = 6
x + 3 y = 12
a) The values of x = -6 and y = 6 satisfy both the equations; therefore, (-6, 6) is the solution
b) The equations have y-intercepts at 2 and 4; therefore (2, 4) is the solution
c) The equations have x-intercepts at 3 and 12; therefore (3,12) is the solution
d) the lines representing the equations intersect at x = 1 and y = 0; therefore (1,0) is the solution

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Abdulazeez10 Abdulazeez10 · Answer 1 · 2022-06-17T18:55:36+02:00

The values of x = -6 and y = 6 satisfy both the equations; therefore, (-6, 6) is the solution. The correct option is a)

From the question, we are to determine the solution of the given system of equations

The given system of equations are

2 x + 3 y = 6 ------- (1)

x + 3 y = 12 ------- (2)

From equation (2)

x + 3y = 12

Then, we can write that

x = 12 - 3y --------- (3)

Substitute this into equation (1)

2x + 3y = 6

2(12 -3y) + 3y = 6

24 - 6y + 3y = 6

24 -3y = 6

24 - 6 = 3y

18 = 3y

∴ y = 18/3

y = 6

Substitute the value of y into equation (3) to get the value of x

x = 12 - 3y

x = 12 -3(6)

x = 12 - 18

x = -6

∴ x= -6 and y = 6 ; Thus, (-6, 6) is a solution

Hence, the values of x = -6 and y = 6 satisfy both the equations; therefore, (-6, 6) is the solution. The correct option is a)

Learn more on Simultaneous linear equations here: https://brainly.com/question/16863577

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