Question

7x+3y=-25

-7x+9y=-47

Answer 1

[AI-generated answer — Bot GPT 3.5]

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

First, we will multiply the first equation by 7 and the second equation by 1 to make the x coefficients add up to 0 when we add the equations together.

7(7x + 3y) = 7(-25)
-7(-7x + 9y) = -7(-47)

49x + 21y = -175
7x - 9y = 47

Now, add the equations together:

49x + 21y + 7x - 9y = -175 + 47
56x + 12y = -128

Now, we can solve for y by isolating y in the equation:

12y = -128 - 56x
12y = -56x - 128
y = (-56x - 128) / 12
y = -14/3x - 32/3

Next, substitute y back into one of the original equations to solve for x. Let's use the first equation:

7x + 3(-14/3x - 32/3) = -25
7x - 14x - 32 = -25
-7x - 32 = -25
-7x = 7
x = -1

Finally, substitute x back into the equation we found for y:

y = -14/3(-1) - 32/3
y = 14/3 - 32/3
y = -18/3
y = -6

Therefore, the solution to the system of equations is x = -1 and y = -6.

Answer 2

Solve the system of equations -x+6y=13

4x-10y=-10

Answer 3

[AI-generated answer — Bot GPT 3.5]

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution in this case.

We are given the system of equations:
1. -x + 6y = 13
2. 4x - 10y = -10

Let's solve for x in the first equation:

-x + 6y = 13
x = 6y + 13

Now, substitute x = 6y + 13 into the second equation:

4(6y + 13) - 10y = -10
24y + 52 - 10y = -10
14y + 52 = -10
14y = -62
y = -62/14
y = -31/7

Now, substitute y = -31/7 back into the equation x = 6y + 13:

x = 6(-31/7) + 13
x = -186/7 + 13
x = -186/7 + 91/7
x = -95/7

Therefore, the solution to the system of equations is x = -95/7 and y = -31/7.