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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

Respuesta :

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

Simultaneous linear equation

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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