Given x2+2xy+4x=−3 and 9y2+4xy+12y=−1. The value of x+3y is....
Explanation
Add the two equations
x29y2x2+++2xy4xy6xy+++4x12y9y2==+−3−14x++12y=−4
Since we are asked for the value of x+3y, we use the substitution x+3y=p
x2+6xy+9y2+4x+12y=−4
x2+6xy+9y2+4(x+3y)=−4
Apply factorization
(x+3y)2+4(x+3y)=−4
p2+4p=−4
p2+4p+4=0
(p+2)2=0
Take the square root of both sides
p+2=0
p=−2
This means x+3y=p→x+3y=−2.