Question

Solve the system of equations by multiplying and adding. braceleftze −6x + 9y = −39 8x + y = 0 Write the solution as an ordered pair: . If necessary, write the answer in fraction form.

Answer 1

`((1)/(2),-4 )`

Explanation:

the system of equations is:

`-6x+9y=-39\\8x+y=0`

First, we multiply the second equation by -9:

`-9(8x+9y=0)\\-72x-9y=0`

and now we add this to the first original equation:

`-6x+9y=-39\\-72x-9y=0\\-------\\-78x+0y=-39`

we have eliminated the y variable, so we can solve for x:

`-78x=-39\\x=-39/(-78)\\x=0.5=(1)/(2)`

with this value of x, we substitute it on the second of the original set of equations to find the value of y:

`8x+y=0\\8(0.5)+y=0\\4+y=0\\y=-4`

the answer as an ordered pair is:

`((1)/(2),-4 )`