Question

Is (2,5) a solution to the system
X + y = 7 2x - 3y = -11
Yes or no show your work to prove the answer is correct

Answer 1

Solve the system of equations using elimination give your answers an ordered pair (x,y)
X + 2y = 10
-6x + 3y = 30
Show your work please

Answer 2

To determine if (2,5) is a solution to the system of equations, we need to plug in the values of x = 2 and y = 5 into each equation and see if the equations hold true.

1. x + y = 7
2 + 5 = 7
7 = 7
This equation holds true when x = 2 and y = 5.

2. 2x - 3y = -11
2(2) - 3(5) = -11
4 - 15 = -11
-11 = -11
This equation also holds true when x = 2 and y = 5.

Therefore, since both equations hold true when x = 2 and y = 5, (2,5) is indeed a solution to the system of equations.

The answer is YES.

Answer 3

To solve the system of equations using the elimination method:

1. Multiply the first equation by 3 and the second equation by 2 to eliminate the y variable:
3(x + 2y) = 3(10)
2(-6x + 3y) = 2(30)

This leads to:
3x + 6y = 30
-12x + 6y = 60

2. Add the two resulting equations to eliminate y:
(3x + 6y) + (-12x + 6y) = 30 + 60
-9x = 90
x = -10

3. Substitute x = -10 back into the first equation:
-10 + 2y = 10
2y = 20
y = 10

Therefore, the solution to the system of equations is:
(-10, 10)