To solve the system of equations, we can use either substitution or elimination.
Using substitution:
Solve one of the equations for one of the variables:
10x + 3y = -11
3y = -10x - 11
y = (-10/3)x - 11/3
Substitute this expression for y into the other equation and solve for x:
8x + 2y = -6
8x + 2((-10/3)x - 11/3) = -6
8x - (20/3)x - 22/3 = -6
(24/3)x - (20/3)x = -6 + 22/3
(4/3)x = -4/3
x = -1
Substitute this value of x back into one of the original equations and solve for y:
10x + 3y = -11
10(-1) + 3y = -11
-10 + 3y = -11
3y = -1
y = -1/3
Therefore, the solution to the system of equations is (x,y) = (-1,-1/3).
Using elimination:
Multiply the first equation by -2:
-20x - 6y = 22
Add this to the second equation:
8x + 2y = -6
-20x - 6y = 22
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-12x = 16
Divide both sides by -12:
x = -4/3
Substitute this value of x into one of the equations and solve for y:
10x + 3y = -11
10(-4/3) + 3y = -11
-40/3 + 3y = -11
3y = -11 + 40/3
3y = -1/3
y = -1/9
Therefore, the solution to the system of equations is (x,y) = (-4/3,-1/9).
10x + 3y = -11 8x + 2y = -6
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