Question

Using complete sentences, explain which method you would use to solve the following system of equations and why you chose that method.

Please show the work.
3x + 2y = 7
4x – 3y = –2

Answer 1

Well, it would help to know what methods you are familiar with. Are you familiar only with elimination, or have you gone into matrices and whatnot?

Answer 2

I would choose elimination because substitution involves fractions and integers are easier to work with.

Answer 3

ok

Answer 4

I forgot how you set it up for elimination method

Answer 5

Subtract or add a multiple of one equation to the other as to eliminate one of the variables entirely, solve for the other, and then back-substitute into one equation to solve for the variable you originally eliminated.

Answer 6

Since the y coefficients have opposite signs, multiply the top equation by 3 and get: 9x+6y = 21
Multiply the second equation by 2 and get: 8x - 6y = -4
now add the two equations and get: 17x = 17 or x = 1. substitute 1 in place of x in either equation and get y = 2

Answer 7

I would use the method of elimination as it is the easiest way to solve the equation in my opinion although you can also use the method of substitution instead

I will post the method now

Answer 8

ok

Answer 9

lilg132?

Answer 10

3x + 2y = 7
4x – 3y = –2

To get one of the variables alone we need to cancel the other variable out

so we multiply both equations by something to make the variables the same value
so we do

3x + 2y = 7 (multiply by 3)
4x - 3y = -2 (multiply by 2)

so you would get

9x + 6y = 21
8x - 6y = -4

so now we have Y the same value and we add the equations together to cancel out y
so we get

17x = 17

to get x on its own we have to get rid of the number next to x

so we divide both sides by 17
which gives you

17x / 17 = 17 / 17

so you would get

x = 1

now we know the value of x we can use this to work out y
so we use it on the second equation although you can choose to use it in the first equation any way would work
lets decide to use it on the second equation
which is

4x – 3y = –2

so you would get

4(1) - 3y = -2

which gives you

4 - 3y = -2

rearrange the formula to get the y variable on its own and the numbers on the other side
so you would get
remember bringing a number to the other side will change its value to the opposite(e.g. bringing -2 to the other side will give you +2)

4 + 2 = 3y

so you get

6 = 3y

and to get y on its own you have to divide both sides by the number next to y
which gives you

6 / 3 = 3y / 3

so you get

2 = y

so the answers are:

y = 2
x = 1

and to check you just use the two values we have found now in any of the equations and check to see you get the same answer as you do in the equation
lets decide to check using the first equation which is

3x + 2y = 7

which gives you

3(1) + 2(2) = 7

3 + 4 = 7

which is correct

now lets check with the second equation just to double check
which is

4x – 3y = –2

so you would get

4(1) - 3(2) = -2

which gives you

4 - 6 = -2

and this equation also works so we have the correct value :)

please dont forget to click good answer and sorry for taking long i made a mistake the first time and had to start again :p