Question

find each value of a and b solving the linear equationsx-w=2y-z+w=3az=1y+bw=0

Equations and inequalities
ANSWERED
asked 2021-03-06

find each value of a and b solving the linear equations
\(x-w=2\)
\(y-z+w=3\)
\(az=1\)
\(y+bw=0\)

Answers (1)

2021-03-07

Given linear equations are,
\(x-w=2, y-z+w=3, az=1, y+bw=0\)
Step 2
To find values of a and b.
Given equations are
\(x-w=2...(1)\)
\(y-z+w=3...(2)\)
\(az=1...(3)\)
\(y+bw=0...(4)\)
from equation(3) \(z=1/a\)
from equation(1)\(w=x-2\)
substitute value of z and \(w in (2)\)
\(y-1a+x-2=3\)
\(\Rightarrow ay-1+ax-2a+3a\)
\(\Rightarrow ay-1+ax-5a=0\)
\(\Rightarrow ay+ax-5a=1\)
\(\Rightarrow a(y+x-5)=1\)
\(\Rightarrow a=1/(y+x-5)\)
from equation (4) \(y+bw=0 \Rightarrow y=-bw\)
\(\Rightarrow b=(-y)/w\)
substitute \(w=x-2\ in\ b=(-y)/w\)
\(\Rightarrow b=(-y)/(x-2)\)
Therefore the values of a and b are
\(a=1/(y+x-5),b=(-y)/(x-2)\)

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