The value of b in the expression is -2.
a + a + b = 14
b + b + c = 8
a + b + c = 18
Therefore,
2a + b = 14
2b + c = 8
c = 8 - 2b
Hence,
a + b + 8 - 2b = 18
a - b = 18 - 8
a - b = 10
2a + b = 14
a - b = 10
3a = 24
a = 8
8 - b = 10
b = 8 - 10
b = -2
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Answer:
a = 8
b = -2
c = 12
Step-by-step explanation:
a + a + b = 14
2a + b = 14 ⇒ ( 1 )
b + b + c = 8
2b + c = 8 ⇒ ( 2 )
a + b + c = 18 ⇒ ( 3 )
First, let us make a as the subject in equation 1.
2a + b = 14
2a = 14 - b
[tex]a=\frac{14-b}{2} \\a = 7-\frac{b}{2}[/tex] ⇒ ( 4 )
Let us make c as the subject in equation 2.
2b + c = 8
c = 8 - 2b ⇒ ( 5 )
Now it is clear for us that, we can replace a & c with ( 7 - b / 2 ) & ( 8 - 2b ) respectively.
And now let us solve the equation 3 to find the value of b.
[tex]a+b+c=18\\\\7-\frac{b}{2} +b+8-2b=18\\\\Combine\: \:like\:\: terms.\\\\[/tex]
[tex]15-\frac{b}{2} -b=18\\\\\frac{15*2}{1*2} -\frac{b}{2}-\frac{b*2}{1*2}=18\\\\\frac{30}{2} -\frac{b}{2}-\frac{2b}{2}=18\\\\\frac{30-3b}{2} =\frac{18}{1} \\\\Use\:\: cross\;\: multiplication[/tex]
[tex]30-3b=18*2\\\\30-3b=36\\\\30-36=3b\\\\-6=3b\\\\-2 = b[/tex]
And now let us find the value of a
For that, let us use the equation 1. There, we can replace b with ( -2 ) to find the value of a.
[tex]2a+b=14\\\\2a-2=14\\\\2a = 14+2\\\\2a=16\\\\a=8[/tex]
Now, let us find the value of c.
For that, let us take the equation 2. There also, we can replace b with -2 to find the value of c.
[tex]2b+c=8\\\\2*-2+c=8\\\\-4+c=8\\\\c=8+4\\\\c=12[/tex]
