(1.)  2x + y = 7

3x - y = 3                   here is the problem
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____    ____
5       5       divide each side by 5

x = 2          divide and cancel

2(2) + y = 7  replace x with 2

4 + y = 7       multiply

-4      -4     subtract 4 from each side
_________________
y = 3        subtract

result:  x = 2 and y = 3

(2.)  a + 5b = 10

-a + 4b = 8                      here is the problem
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___  ___
9     9           divide each side by 9

b = 2               divide and cancel

a + 5(2) = 10               replace b with 2

a + 10 = 10             multiply

-10  -10         subtract 10 from each side
_________________
a         = 0         subtract

result:  a = 0 and b = 2

(3.)  7x + 3y = 19

4x - 3y = 3                 here is the problem
___________________
____     ___
11      11             divide each side by 11

x = 2             divide and cancel

7(2) + 3y = 19          replace x with 2

14 + 3y = 19              multiply

-14       -14    subtract 14 from each side
_________________
3y = 5          subtract
___ __
3  3          divide each side by 3

y = 5/3            cancel

result:  x = 2  and y = 5/3

(4.)  -7c - 8d = 8

7c - 8d = 8                here is the problem
___________________
_____  ____
-16   -16          divide each side by -16

d = -2             divide and cancel

7c - 8(-2) = 8          replace d with -2

7c + 16 = 8                 multiply

-16   -16      subtract 16 from each side
___________________
7c      = -8      subtract
___      ___
7        7      divide each side by 7

c = -8/7           cancel

result:  c = -8/7 and d = -2

(5.)  x + 3y = 9

-x + 2y = 6                    here is the problem
___________________
___ ____
5  5            divide each side by 5

y = 3              divide and cancel

x + 3(3) = 9           replace y with 3

x + 9 = 9            multiply

-9 -9        subtract 9 from each side
________________
x      = 0       subtract

result:  x = 0 and y = 3

(6.)  (3/4)x - (1/2)y = 4

(1/4)x + (1/2)y = 2.5              here is the problem
_____________________________

(1/4)(6.5) + (1/2)y = 2.5   replace x with 6.5

1.625    + (1/2)y = 2.5      multiply

-    1.625          -   1.625   subtract 1.625 from
______________________________   each side
(1/2)y =   0.875      subtract

2(1/2)y = (2)(0.875)   multiply each side by 2

y = 1.75             multiply

result:  x = 6.5   and   y = 1.75

(7.)  (1/2)x + y = 9

(3/4)x - y = 0                here is the problem
___________________
_______     ___
1.25       1.25           divide each side by 1.25

x = 7.2             divide and cancel

(1/2)(7.2) + y = 9           replace x with 7.2

3.6 + y = 9             multiply

-3.6    -3.6        subtract 3.6 from each side
_____________________

y = 5.4         subtract

result:  x = 7.2  and y = 5.4

(8.)  0.4x + y = 1.2

0.6x - y = 3.9              here is the problem
_______________________

0.4(5.1) + y = 1.2     replace x with 5.1

2.04 + y = 1.2            multiply

-2.04    - 2.04       subtract 2.04 from each side
_______________________
y = -0.84       subtract

result:   x = 5.1 and y = -0.84

(9.)  2x - 3y = 8

2x + 3y = 4                here is the problem
________________
____    ____
4         4        divide each side by 4

x = 3          divide and cancel

2(3) + 3y = 4       replace x with 3

6 + 3y = 4               multiply

-6      -6      subtract 6 from each side
__________________
3y = -2       subtract
____ ____
3     3    divide each side by 3

y = -2/3         cancel

result:  x = 3 and y = -2/3

(10.)   7a + 6b = 0

15a - 6b = 0            here is the problem
__________________
____     _____
22        22     divide each side by 22

a = 0               divide and cancel

7(0) + 6b = 0          replace a with 0

6b = 0           multiply and add
____  ___
6    6      divide each side by 6

b = 0         divide and cancel

result:  a = 0 and b = 0