Question

Solve by using substitution or elimination by addition

2x - 5y = 27

3x + 2y = -7


Select the correct choice below and fill in the answer box within your choice.


A.The unique solution to the system is ___ ​(Type an ordered​ pair.)

B.There are an infinite number of solutions.

C.There is no solution.

Answer 1

Answer: A. The unique solution to the system is
`(1,-5)`

Explanation:

You can follow these steps to solve the system of equations by the Elimination Method:

- Multiply the first equation by -3 and the second equation by 2.

- Add both equations and solve for "y".

Then:

`\left \{ {{-3(2x - 5y) = -3(27)} \atop {2(3x + 2y)= 2(-7)}} \right.\\\\\left \{ {{-6x +15y = -81} \atop {6x + 4y= -14}} \right.\\..............................\\19y=-95\\y=-5`

- Substitute the value of "y" into any original equation to find the value of "x". Then:

`2x - 5(-5) = 27\\\\2x=27-25\\\\2x=2\\\\x=1`

Therefore, the unique solution to the system is
`(1,-5)`