Question

Without graphing, tell whether the system has one solution, no solution or many solutions.(pic attached)

Answer 1

you can eliminate a variable or substitute? which would you like?

Answer 2

subst.

Answer 3

alright for substitution you want to take the first equation and solve for x or y. the easiest way would to be to solve for y since it has a coefficient of (-1) soon to be 1

Answer 4

-2x-y=9

(add y to both sides of the equation)

-2x-y+y=9+y

-2x=9+y

(subtract 9 from both sides of equations)

-2x-9=9-9+y

-2x-9=y

(now that you have the equation solved for y, you want to replace y with f(x) (-2x-9) in g(x) or the second function (3x-4y=-8).)

3x-4(-2x-9)=-8

(distribute)

3x+8x+36=-8

11x+36=-8

(subtract 36 from both sides)

11x+36-36=-8-36

11x=-44

(divide both sides by 11)

x=-4

(now that you know x=-4 go back to your first y= equation and simply put -4 in for x)

y=-2(-4)-9

y=8-9

y=-1

Answer 5

so im guessing there are many solutions? cause my answer choices are one no solutions or many

Answer 6

to check simply put y=-1,x=-4 into one of the equations or both if you want to

-2(-4)-(-1)=9

8-(-1)=9

8+1=9

9=9

Answer 7

there is only one set of solutions

Answer 8

inorder to have more than one solution you have to have a quadratic formula or when you cannot cancel out one of the variables (usually this is a system equations with 3 variables)