# Thread: May someone solve this equations for me?

1. ## May someone solve this equations for me?

X+5y=21
x+3y=11

3x+y=13
5x+2y=7

2. Originally Posted by thebesta1
X+5y=21
x+3y=11

3x+y=13
5x+2y=7
x+5y=21
x+3y=11

x=21-5y (isolate x)

sub the value of x to 2nd equation to solve for y

21-5y+3y=11

-2y=-10

y=5

substitute the value of y into the other equation to solve for x

x+5(5)=21

x+25=21

x=-4

Do you see what I did? Now follow the same method for solving the second one and show me what you get

3. Originally Posted by thebesta1
X+5y=21
x+3y=11

3x+y=13
5x+2y=7
from this
1x + 5y = 21
1x + 3y = 11

1 5
1 3

1*3 - 1*5 = 3-5 = -2
the determinant of the equation

Then find the determinant of a replacement:
replace the constants of the variable x:

21 5
11 3

21*3 - 11-5 = 63 - 55 = 8

Then divide this determinant with the system determinant:

8 / -2 = -4

Thus x = -4

Then do the same and replace the constant of y:

1 21
1 11

1*11 - 21*1 = 11 - 21 = -10

-10 / -4 = 2.5
thus y = 2.5