The solution to�=12�+2y=21​x+2 and�=−14�+8y=−41​x+8

Answer 1

To find the solution to the system of equations:
12x + 2y = 21x + 2
-14x + 8y = -41x + 8

We need to solve one equation for a variable and substitute it into the other equation.

From the first equation, we can solve for x:

12x = 21x + 2y - 2
-9x = 2y - 2
x = (2y - 2) / -9

Now we substitute this value of x into the second equation:

-14(2y - 2) / -9 + 8y = -41(2y - 2) / -9 + 8
28y - 28 / 9 + 8y = 82y - 82 / 9 + 8
36y - 28 / 9 = 82y - 82 / 9
-46y = -54 / 9
-46y = -6
y = -6 / -46
y = 3 / 23

Now we substitute this value of y back into x = (2y - 2) / -9:

x = (2(3 / 23) - 2) / -9
x = (6 / 23 - 2) / -9
x = (6 / 23 - 46 / 23) / -9
x = -40 / 23 / -9
x = -40 / 23 * -1 / 9
x = 40 / 207

Therefore, the solution to the system of equations is x = 40/207 and y = 3/23.