Question

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

Equations and inequalities

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

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
$$a=1/(y+x-5),b=(-y)/(x-2)$$