Question

2x+8y=8

2x-4y=-16

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve this system of equations, we can use the method of substitution.

From the first equation:
2x + 8y = 8
Solving for x:
2x = 8 - 8y
x = 4 - 4y

Now, substitute x in the second equation:
2x - 4y = -16
2(4 - 4y) - 4y = -16
8 - 8y - 4y = -16
8 - 12y = -16
-12y = -24
y = 2

Now substitute y back into the first equation to solve for x:
2x + 8(2) = 8
2x + 16 = 8
2x = -8
x = -4

Therefore, the solution to the system of equations is x = -4 and y = 2.

Answer 2

7x+3y=-25

-7x+9y=-47

Answer 3

[AI-generated answer — Bot GPT 3.5]

To solve this system of equations, we can use the method of elimination.

1. Multiply the first equation by 7 and the second equation by -1 to eliminate x:
7(7x+3y)=-7(25)
-(-7x+9y)=47

Expanding, we get:
49x + 21y = -175
7x - 9y = 47

2. Add the two equations together to eliminate x:
49x + 21y + 7x - 9y = -175 + 47
56x + 12y = -128

3. Solve for y:
12y = -56x - 128
y = -56/12 x - 128/12
y = -14/3 x - 32/3

4. Substitute y back into the first equation to solve for x:
7x + 3(-14/3 x - 32/3) = -25
7x - 14x - 96 = -75
-7x = 21
x = -3

5. Substitute x back into the equation y = -14/3 x - 32/3:
y = -14/3 * (-3) - 32/3
y = 14 - 32/3
y = -32/3

Therefore, the solution to the system of equations is x = -3 and y = -32/3.