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Solve for x, y, z, a, b, c, d
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2\left(x-11\right)+3\left(9+1\right)=-4
Consider the second equation. Multiply both sides of the equation by 6, the least common multiple of 3,2.
2x-22+3\left(9+1\right)=-4
Use the distributive property to multiply 2 by x-11.
2x-22+3\times 10=-4
Add 9 and 1 to get 10.
2x-22+30=-4
Multiply 3 and 10 to get 30.
2x+8=-4
Add -22 and 30 to get 8.
2x=-4-8
Subtract 8 from both sides.
2x=-12
Subtract 8 from -4 to get -12.
x=\frac{-12}{2}
Divide both sides by 2.
x=-6
Divide -12 by 2 to get -6.
\frac{-6-1}{2}-\frac{y-1}{3}=-\frac{13}{30}
Consider the first equation. Insert the known values of variables into the equation.
15\left(-6-1\right)-10\left(y-1\right)=-13
Multiply both sides of the equation by 30, the least common multiple of 2,3,30.
15\left(-7\right)-10\left(y-1\right)=-13
Subtract 1 from -6 to get -7.
-105-10\left(y-1\right)=-13
Multiply 15 and -7 to get -105.
-105-10y+10=-13
Use the distributive property to multiply -10 by y-1.
-95-10y=-13
Add -105 and 10 to get -95.
-10y=-13+95
Add 95 to both sides.
-10y=82
Add -13 and 95 to get 82.
y=\frac{82}{-10}
Divide both sides by -10.
y=-\frac{41}{5}
Reduce the fraction \frac{82}{-10} to lowest terms by extracting and canceling out 2.
z=-6-1-2\left(-\frac{41}{5}\right)
Consider the third equation. Insert the known values of variables into the equation.
z=-7-2\left(-\frac{41}{5}\right)
Subtract 1 from -6 to get -7.
z=-7+\frac{82}{5}
Multiply -2 and -\frac{41}{5} to get \frac{82}{5}.
z=\frac{47}{5}
Add -7 and \frac{82}{5} to get \frac{47}{5}.
a=\frac{47}{5}
Consider the fourth equation. Insert the known values of variables into the equation.
b=\frac{47}{5}
Consider the fifth equation. Insert the known values of variables into the equation.
c=\frac{47}{5}
Consider the equation (6). Insert the known values of variables into the equation.
d=\frac{47}{5}
Consider the equation (7). Insert the known values of variables into the equation.
x=-6 y=-\frac{41}{5} z=\frac{47}{5} a=\frac{47}{5} b=\frac{47}{5} c=\frac{47}{5} d=\frac{47}{5}
The system is now solved.