How do solve the following linear system?: 4x+3y=1 , -6x-2y=-8 ?

1 Answer

the solution is:

(x,y)-=(2.2,-2.6)

Explanation:

4x+3y=1------(1)

-6x-2y=-8------(2)

If
a11x+a12y=b11
a21x+a22y=b21

Then,

x=(b11a22-b21a12)/(a11a22-a21a12)

y=(a11b21-a21b11)/(a11a22-a21a12)

Here,

a11=4; a12=3; b11=1

a21=-6; a22=-2; b21=-8

Substituting

x=(1xx(-2)-(-8)xx3)/(4xx(-2)-(-6)xx3)=(-2+24)/(-8+18)=22/10=2.2

y=(4xx(-8)-(-6)xx1)/(4xx(-2)-(-6)xx3)=(-32+6)/(-8+18)=-26/10=-2.6

Check:

lhs=4x+3y=4xx2.2+3xx(-2.6)=8.8-7.8=1=rhs

lhs=-6x-2y=-6xx2.2-2xx(-2.6)=-13.2+5.2=-8=rhs

Hence,
the solution is:

(x,y)-=(2.2,-2.6)