Question

what values of a and b make the given statement true? (ay^2+3xy-9x^2)-(-4y^2+8xy+bx^2)=10y^2-5xy-10x^2

Answer 1

Given :

$(ay^2 + 3xy -9x^2) - (-4y^2+8xy +bx^2) = 10y^2 -5xy -10x^2 \\\\ay^2 + 3xy - 9x^2 + 4y^2 -8xy -bx^2 = 10 y^2 -5xy -10x^2$

Grouping like terms together, we have$(a+4)y^2 -5xy -(9+b)x^2 = 10y^2 -5xy -10x^2$

Equating the like terms on both sides of the equation, we have

$a+4 =10 \implies a=6 \\\\9+b = 10 \implies b=1$

∴ $a=6 ; b=1$

Answer 2

we are given

(ay^2 + 3xy -9x^2) - (-4y^2+8xy +bx^2) = 10y^2 -5xy -10x^2 \\\\ay^2 + 3xy - 9x^2 + 4y^2 -8xy -bx^2 = 10 y^2 -5xy -10x^2

Group like terms together, we have(a+4)y^2 -5xy -(9+b)x^2 = 10y^2 -5xy -10x^2

Equating the like terms on both sides of the equation, we have

a+4 =10 gives

a=6

similarly 9+b = 10  

gives b=1

a=6 ; b=1