Question

Solve for the following system of equations.

-7x+6y=9
-2x-5y+16

x=?
y=?

Answer 1

`x=-3\\\\y=-2`

Explanation:

Given the system of equations
`\left \{ {{-7x+6y=9} \atop {-2x-5y=16}} \right.`, you can use the Elimination Method to solve it.

You can multiply the first equation by -2 and the second equation by 7, then add both equations and solve for the variable "y":

`\left \{ {{14x-12y=-18} \atop {-14x-35y=112}} \right.\\...........................\\-47y=94\\\\y=(94)/(-47)\\\\y=-2`

Substitute the value of "y" into any original equations and solve for the variable "x". Then:

`-7x+6y=9\\\\-7x+6(-2)=9\\\\-7x-12=9\\\\-7x=9+12\\\\x=(21)/(-7)\\\\x=-3`

Answer 2

x = -3 and y = -2

Explanation:

It is given that,

-7x + 6y = 9 ----(1)

-2x - 5y = 16 -------(2)

To find the solution of given equations

eq(1) * 2 ⇒

-14x + 12y = 18 ------(3)

eq(2) * 7 ⇒

-14x - 35y = 112 ---(4)

eq (3) - eq(4) ⇒

-14x + 12y = 18 ------(3)

-14x - 35y = 112 ---(4)

0 4y = -94

y = 94/(-47) = -2

Substitute the value of y in eq (2)

-2x - 5y = 16 -------(2)

-2x - 5*-2 = 16

-2x +10 = 16

-2x = 6

x = 6/-2 = -3

Therefore x = -3 and y = -2