Question

Solve this system of equations:

`x-2y=3`
`3x+y=-5`
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Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve this system of equations using the method of elimination, we can multiply the first equation by 3 and the second equation by 2 to create coefficients that will cancel each other out when we add the two equations together.

First equation: `3(x-2y) = 3(3)`
-> `3x - 6y = 9`

Second equation: `2(3x + y) = 2(-5)`
-> `6x + 2y = -10`

Now we can add these two equations together:
`(3x - 6y) + (6x + 2y) = 9 + (-10)`
-> `9x - 4y = -1`

Now we have a new equation: `9x - 4y = -1`

Next, we can use either substitution or elimination to solve for one variable and substitute that value back into one of the original equations to solve for the other variable.

Let's use substitution here. We can solve the first equation for x and substitute this expression for x in the new equation:

From the first equation: `x = 2y + 3`

Substituting this into the new equation: `9(2y + 3) - 4y = -1`
-> `18y + 27 - 4y = -1`
-> `14y + 27 = -1`

Now, let's solve for y:
-> `14y = -1 - 27`
-> `14y = -28`
-> `y = -28/14`
-> `y = -2`

Now that we have the value of y, we can substitute it back into the first equation to solve for x:

From first equation: `x - 2(-2) = 3`
-> `x + 4 = 3`
-> `x = 3 - 4`
-> `x = -1`

Therefore, the solution to the system of equations is x = -1 and y = -2.