How do I solve for x and y?

Question

Please help, My notes on this seem to be wrong (they had a lot of steps and I think I missed some)

2x+3y=7
5x-y=9

Does the formula work for all other types of these?

the question states "solve for x and y in each of the following systems of equations"

Answer 1

Do both of those equations relate? Then use Systems of Equations:

2x+3y=7
5x-y=9

Multiply one of the equations by a factor that will lead to one of the variables dropping out. I am multiplying the second one by 3.

2x+3y=7
15x-3y=27

Now add the two equations up, it is easiest to do when they are on top of each other.

2x+3y=7
15x-3y=27
Becomes:
17x = 34

Then solve for x
17x = 34
x = 2

Now that you know x you can plug x into one of the equations to find y. I like the second one better, since y isn't multiplied by anything.

5x-y=9
Put x=2 in
10 - y = 9
-y = -1
y = 1

So, x=2 and y=1

This method works for all the kinds of equations like this. I am not sure what you mean by a formula?

Answer 2

2x + 3y = 7
5x - y = 9

Substitution is probably the easiest to see.
5x - y = 9 becomes
y = 5x - 9

2x + 3y = 7 then becomes
2x + 3(5x - 9) = 7
2x + 15x - 27 = 7
17x = 34
x = 2
y = 5*2 - 9
y = 1

Alternatively, you can multiply the 2nd equation by 3 (the coefficient of y in the 1st equation) to get
15x - 3y = 27. Add the 1st equation:
2x + 3y = 7
3y - 3y = 0, so
17x = 34, which is what we got above.

Lastly, you have the generalized matrix-determinate form
x = (7*(-1) - 9*3) / (2*(-1) - 5*3)
x = (-7 - 27) / (-2 - 15)
x = -34/-17
x = 2
y = (2*9 - 5*7) / (2*(-1) - 5*3)
y = (18 - 35) / -17
y = -17 / -17
y = 1

Answer 3

From the 1st equation,

2x + 3y = 7
x = (7-3y) / 2 -----> use this in the 2nd equation to solve 'y'

i.e.

5 [ (7-3y) / 2 ] -y = 9
[(35 - 15y) /2 ] - 2y/2 = 9
35 - 15y - 2y = 18
-17y = -17
y= -17 / -17
y = 1 ----> use this to solve 'x' using any of the original equations

2x + 3 (1) = 7
2x = 7 -3
2x = 4
x = 2

You know your answers are correct when u use back your answers in the 2 equations, it will give the answers given

Answer 4

solve by substitution

5x - y = 9

5x - 9 = y

substitute this equation in for y into the first equation

2x + 3 (5x - 9) = 7

17x - 27 = 7

x = 2 ;
substitute x into any equation
5x - y = 9

y = 1

therefore
x= 2, y = 1

Answer 5

to solve for y
5(2x+3y=7) which is 10x+15y=35

-2(5x-y=9) which is -10x+2y= -18
then
10x + 15y = 35
+ (-10X) + 2y = -18
________________________
0x + 17y = 17
therefore y=1

plug 1 for y into either of the original equations to solve for x

you should get x=2

Answer 6

2x + 3y = 7
5x - y = 9

5x - y = 9
-y = -5x + 9
y = 5x - 9

2x + 3(5x - 9) = 7
2x + 15x - 27 = 7
17x = 34
x = 2

y = 5(2) - 9 = 10 - 9 = 1

ANS : (2,1)