Given the system of equations, what is the solution? 2x + 3y = 2 3x - 4y = 20

x = 4 and y = - 2

Step-by-step explanation:

First equation: 2x + 3y = 2.

Second equation: 3x - 4y = 20.

Using the substitution method:

From Equation 1:

3y = 2 - 2x.

y = (2 - 2x) / 3 (Equation 3).

Put equation 3 in equation 2:

3x - 4 (2-2x) / 3 = 20.

Taking LCM:

(9x - 4 (2-2x)) / 3 = 20.

Cross Multiplying:

9x - 8 + 8x = 60

17x = 68

x = 4.

Put x = 4 in Equation 3:

y = (2 - 2 (4)) / 3

y = (2-8) / 3 = - 6/3 = - 2.

Therefore, x = 4 and y = - 2!