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1. 5x - y = 7

x = 2

y = 3

5(2) - 3

10 - 3

= 7

2. -3x - 2y = 12

x = 2

y = 3

-3(2) - 2(3)

-6 - 6

= -12

x = 2

y = 3

5(2) - 3

10 - 3

= 7

2. -3x - 2y = 12

x = 2

y = 3

-3(2) - 2(3)

-6 - 6

= -12

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Using substitution method to get the answer provided by Awesome Helper (and I hope that this solution stays here. Thank you.)

Equation 1) 5x - y = 7

Equation 2) - 3x - 2y = -12

Step 1, using Equation 1

5x - y = 7

-y = -5x + 7

y = 5x - 7

Equation 3: y = 5x - 7

Step 2: Using Equation 2, substitute 5x-7 for y

-3x - 2y = -12

-3x - 2 (5x - 7) = -12

- 3x - 10x + 14 = -12

-13x = -12 - 14

__-13x __= __-26__

-13 -13

x = 2

Step 3, Using Equation 3, substitute 2 for x

y = 5x - 7

y = 5 (2) - 7

y = 10 - 7

y = 3

The solution to this system is x = 2; y = 3

Equation 1) 5x - y = 7

Equation 2) - 3x - 2y = -12

Step 1, using Equation 1

5x - y = 7

-y = -5x + 7

y = 5x - 7

Equation 3: y = 5x - 7

Step 2: Using Equation 2, substitute 5x-7 for y

-3x - 2y = -12

-3x - 2 (5x - 7) = -12

- 3x - 10x + 14 = -12

-13x = -12 - 14

-13 -13

x = 2

Step 3, Using Equation 3, substitute 2 for x

y = 5x - 7

y = 5 (2) - 7

y = 10 - 7

y = 3

The solution to this system is x = 2; y = 3