System of equations using addition or subtraction:

Solve the subsequent system of equations using addition or subtraction.

5x + 6y = 12

3x + 5y = 3

Solution:

Step 1. Make the coefficients of y equal within both equations by multiplying the first equation by 5 and the second equation by 6.

5(5x + 6y = 12) yields 25x + 30y = 60

6(3x + 5y = 3)  yields 18x + 30y = 18

Step 2. Subtract the second equation from the first.

25x + 30y = 60

-(18x + 30y =18)

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7x + 0  = 42

Step 3. Solve the resulting equation.

7x        = 42

7x/7     = 42/7

X =  6

Step 4. Substitute x = 6 into one of the original equations and solve for y.

5x + 6y = 12

5(6) + 6y = 12

30 + 6y =12

6y = 12- 30

6y = -18

6y/6 =   -18/6

y = -3

Step 5. Check the solution by substituting x = 6 and y = -3 into the other original equation.

3x + 5y = 3

3(6) +5 (-3) = 3

18-15 = 3

3=3

Therefore, the solution checks.