7x + y = 1,3x + 2y = -9?

7x + y = 1
y = 1-7x (eq 1)

3x + 2y = -9
3x + 2(1-7x) = -9
3x + 2 - 14x = -9
2+9 = 14x - 3x
11 = 11x
x = 1

plug this into eq 1
7(1) + y = 1
y = 1-7
y = -6

7x + y = 1
3x + 2y = -9

7x + y = 1
y = 1 - 7x

3x + 2y = -9
3x + 2(-7x + 1) = -9
3x - 14x + 2 = -9
3x - 14x = -9 - 2
-11x = -11
x = -11/-11
x = 1

7x + y = 1
7(1) + y = 1
y = 1 - 7
y = -6

∴ x = 1 , y = -6

y = 1 - 7x

3x + 2 - 14x = - 9
- 11 x = - 11
x = 1

y = 1 - 7
y = - 6

x = 1 , y = - 6

1. 7x+y=1 has infinitely many solutions
take 7x on the other side
y=1-7x
put x with diferent values like 1,2,3etc.
if you put x=1 then
y=1-7*1
y=1-7
y=-6
2. 3x+2y=-9
here you can put the value of x nad also y
take 3x on the other side
2y=-9-3x
now again you can put any value of x and you can get your answer
remember every linear equation in two variables has infinitely many solutions

7x+y=1,then y=1-7x,3x+2y=-9,3x+2(1-7x)=-9,3x+2-14x=-9,-11x=-11,
x=1,7+y=1,y=-6.CHECK:
7-6=1,&3-12=-9 so,x=1 and y=-6