Systems of two equations Assignment Help

Assignment Help: >> Simultaneous Equations - Systems of two equations

Systems of two equations :

Systems of two equations involving the two unknowns can also be solved by substitution.

Step 1. Solve one equation for one unknown in terms of the other.

Step 2. Substitute this value within the other equation.

Step 3. Solve the resulting equation for the value of the one remaining unknown.

Step 4. Find out the value of the other unknown by substituting the value of the first unknown into one of the original equations.

Step 5. Check the solution through substituting the values of the two unknowns within the other original equation.

Example:

Solve the subsequent system of equations using substitution.

5x + 6y = 12

3x + 5y = 3

Solution:

Step 1. Solve the first equation for x.

5x + 6y = 12

5x = 12 - 6y

5x/5 = (12- 6y) /5

x = 12/5 - 6y/5

Step 2. Substitute this value of x into the second equation.

3x + 5y = 3

3((12/5) - (6y/5)) +5y = 3

Step 3. Solve the resulting equation.

3(12/5 - 6y/ 5) + 5y = 3

36/5 -18y/5 +5y = 3

(5) ((36/5) -(18/5)y + 5y) = 3(5)

36- 18y +25y = 15

7y = 15-36

7y = -21

(7y/7) = -(21/7)

y = -3

Step 4. Substitute y = -3 into one of the original equations & solve for x.

5x +6y =12

5x +6(-3) = 12

5x -18 = 12

5x = 12 +18

5x = 30

5x/ 5 = 30/5

X = 6

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.

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