Find the solution of the system of equations.
minus, 2, x, minus, 6, y, equals, 8
−2x−6y=
8
minus, 6, x, minus, 6, y, equals, 0
−6x−6y=
0
To find the solution of the system of equations -2x - 6y = 8 and -6x - 6y = 0, we can solve the system by either substitution or elimination method.
Using elimination method:
Step 1: Multiply the second equation by -1/6 to create opposite coefficients for y.
-6 * (-1/6)x - 6 * (-1/6)y = 0 * (-1/6)
x + y = 0
Step 2: Rewrite the first equation and the new second equation.
-2x - 6y = 8
x + y = 0
Step 3: Add the equations together to eliminate x.
(-2x + x) + (-6y + y) = 8 + 0
-1x - 5y = 8
Now, we have the following system:
-1x - 5y = 8
x + y = 0
Step 4: Solve the new system of equations using the method of your choice (substitution or elimination).
-1x - 5y = 8 (Equation A)
x + y = 0 (Equation B)
From Equation B, we can solve for x: x = -y.
Substitute x = -y into Equation A:
-(-y) - 5y = 8
y + 5y = 8
6y = 8
y = 8/6
y = 4/3
Now substitute the value of y = 4/3 into Equation B to solve for x:
x + 4/3 = 0
x = -4/3
Therefore, the solution to the system of equations is x = -4/3 and y = 4/3.