Question

Solve using substitution. (C&D)
2C+3D=1
-3C+D=15

Answer 1

2c + 3d = 1 ⇒ 2c + 3d = 1 ⇒ 2c + 3d = 1
-3c + d = 15 ⇒ 3(-3c + d) = 15 ⇒ -9c + 3d = 15
-7c = 16
-7c = 16
-7 - 7
c = -2 2/7
2(2 2/7) + 3d = 1
4 4/7 + 3d = 1
-4 4/7 -4 4/7
3d = -3 4/7
3d = -3 4/7
3 3
d = -1 4/21
(c, d) = (-2 2/7, -1 4/21)

Answer 2

Equation 2
-3c+d=15
d=15+3c

Substitute into eq 1
2c+3(15+3c)=1
2c+45+9c=1
11c=-44
c=-44/11

c=-4

Sub into eq 1

2(-4)+3d=1
-8+3d=1
3d=9
d=9/3

d=3

Verify:
2(-4)+3(3)=1
-8+9=1
1=1 -- True.