Question

Solve using substitution.

y = x – 2
x + y = 10

7x + 2y = - 8
8y = 4x

Solve using elimination.

2x + 3y = 12
2x – y = 4

5x – 2y = - 19
2x + 3y = 0

Answer 1

x + (x-2) = 10
2 x - 2 = 10
2 x = 12
x = 6
then y = (x-2) = 4

8 y = 4 x is x = 2 y
7(2y) + 2 y = -8
14 y + 2 y = 8
16 y = 8
y = 1/2
then x = 2y = 1

2 x + 3 y = 12
2 x - 1 y = 4
------------------subtract
0 x + 4 y = 8
y = 2
2 x - 2 = 4
x = 3

first line times 3, second times 2
15 x - 6 y = -57
+4 x + 6 y = 0
====================== add
19 x = -57
x = - 3
2(-3) + 3 y = 0
3 y = 6
y = 2

Answer 2

I show you one of them and the other one is your work ;) ..

(i) 7x + 2y = - 8
(ii) 8y = 4x
______________
i take equation (ii) and solve it for x:
8y=4x (divide by 4)
2y=x or x=2y (iii)
____________
now i take (i) and substitute (iii):
7(2y)+2y=-8
14y+2y=-8
16y=-8 (divide by 16
y=-0.5
____________
Now we get x from (iii):
x=2y=2*(-0.5)=-1

-------------------
-------------------

(i) 2x + 3y = 12
(ii)2x – y = 4
----------------
(iii): 4y=8 ((i)-(ii))
(ii): 2x-y=4
----------------
(iii): y=2
insert in (ii): 2x-2=4 -> 2x=6 -> x=3

Answer 3

5x-2y=0

Answer 4

Y=3+x