how to solve by the substitution method problem 1 y=3x+1 3y-5x=11 problem 2 5x-4y=-9 x+4y=3?

1
3 [ 3x + 1 ] - 5x = 11
9x + 3 - 5x = 11
4x = 8
x = 2 , y = 7

2
6x = - 6
x = - 1
4y = 4
y = 1
x = - 1 , y = 1

1.
y = 3x + 1 …… [1]
3y - 5x = 11 …… [2]

Substitute [1] into [2] :
3(3x + 1) - 5x = 11
9x + 3 - 5x = 11
4x = 8
x = 2

Substitute x = 2 into [1] :
y = 3(2) + 1
y = 7

Hence, x = 2, y = 7


====
2.
5x - 4y = -9 …… [1]
x + 4y = 3 …… [2]

From [2] :
x = 3 - 4y …… [3]

Substitute [3] into [1] :
5(3 - 4y) - 4y = -9
15 - 20y - 4y = -9
-24y = -24
y = 1

Substitute y = 1 into [3] :
x = 3 - 4(-1)
x = -1

Hence, x = -1, y = 1

1).
y = 3x + 1
3y - 5x = 11
3(3x + 1) - 5x = 11
4x = 8
x = 2
y = 7
2).
5x - 4y = - 9
x + 4y = 3
x = -1, y = 1

1 y = 3x+1 ..........(1)

3y - 5x = 11.......(2)

Substitute for y in (2)

3(3x + 1) - 5x = 11

9x + 3 - 5x = 11

4x = 8

x = 2

For x = 2, y = 3(2) + 1 = 7

(2, 7)




2 5x - 4y = -9 ............(1)

x + 4y = 3...............(2)

From (1), x = 3 - 4y ......(3)

Substitute for x in (1)

5(3 - 4y) - 4y = - 9

15 - 20y - 4y = - 9

- 24y = - 24

24y = 24

y = 1

Substitute in (1)

5x - 4(1) = - 9

5x - 4 = - 9

5x = - 5

x = - 1

(- 1, 1)