How do you solve this simultaneous equation? 4x+y=4 2x+3y=-3?

4x + y = 4
2x + 3y = -3
5y = -10
y = -2
x = 3/2

4x + y = 4 …… [1]
2x + 3y = -3 …… [2]

From [1] :
y = 4 - 4x …… [3]

Substitute [3] into [2] :
2x + 3(4 - 4x) = -3
2x + 12 - 12x = -3
-10x = -15
x = 3/2

Substitute x = (3/2) into [3] :
y = 4 - 4(3/2)
y = -2

Hence, x = 3/2, y = -2

The second equation can be written as:

2x = -3 - 3y

i.e. 4x = -6 - 6y

Substituting in to the first equation we have:

(-6 - 6y) + y = 4

i.e. -6 - 5y = 4

=> 5y = -10

so, y = -2

Then, 4x - 2 = 4

=> 4x = 6

i.e. x = 3/2

:)>

-12x - 3y = - 12
2x + 3y = - 3_____add

-10x = - 15
x = 5/2

10 + y = 4
y = - 6

x = 5/2 , y = - 6

There is more than one way.

Substitution:
rearrange the first equation to solve for y in terms of x
y = -4x+4

substitute -4x+4 for y in the second equation
2x+3(-4x+4) = -3

solve for x
2x-12x+12 = -3
-10x = -15
x = 3/2

y = -4x+4 = -4(3/2)+4 = -2
:::::
Elimination:
multiply second equation by -2
-4x-6y = 6

add to first equation to eliminate the x terms
 4x+y = 4
-4x-6y = 6
------------
  -5y = 10

y = -2