Solving for y EXAMPLE PROBLEMS Example 1 2

Solving for y EXAMPLE PROBLEMS

Example 1: -2 (x + 3 y) = 18 Procedure Justification - 2 x – 6 y = 18 Distributive property + 2 x - 6 y = 2 x + 18 Eliminating x from one side by adding. Commutative Property -6/-6 Y = -2/6 x + -18/6 Eliminating the coefficient of y by dividing. Y= - 1/3 x - 3 Divide and reduce fractions.

Example 2: 5 x + 10 = 10 y Procedure Justification 10 y = 5 x + 10 Commutative Property 10/10 y = 5/10 x + 10/10 Eliminating the coefficient of y by dividing Divide and reduce fractions. Y = 1/2 x + 1

Example 3: 5 y + 8 = 2 y – 3 x + 5 Procedure -2 y Justification -2 y 3 y + 8 = - 3 x + 5 -8 -8 Eliminating y from one side by subtracting. 3 y = -3 x - 3 Combine like terms. Eliminating constants from one side by subtracting Combine like terms. 3/3 y = -3/3 x – 3/3 Eliminating the coefficient of y by dividing Y = - 1 x - 1 Divide.

Example 4: 3 y = 15 x - 12 Procedure Justification 3/3 y = 15/3 x – 12/3 Eliminating the coefficient of y by dividing Divide. Y = 5 x – 4

Example 5: x + 5 y – 10 = 2 x Procedure -x 5 y – 10 = x + 10 5 y = x + 10 5/5 y = x/5 + 10/5 Y = 1/5 x + 2 -x Justification Eliminating x from one side by subtracting. Combine like terms. Eliminating constants from one side by adding. Combine like terms. Eliminating the coefficient of y by dividing Divide and reduce fractions.

Example 6: 8 x – 4 y = -4 Procedure -8 x -4 y = -8 x - 4 -4/4 y = -8/-4 x – 4/4 Y = 2 x - 1 Justification - 8 x Eliminating x from one side by subtracting. Combine like terms. Eliminating the coefficient of y by dividing Divide.

Example 7: 9 x + 3 y = 3 Procedure -9 x Justification - 9 x 3 y = - 9 x + 3 3/3 y = -9/3 x + 3/3 Y = -3 x + 1 Eliminating x from one side by subtracting. Combine like terms. Eliminating the coefficient of y by dividing Divide.

Example 8: 5(x + y) = 20 + 3 x Procedure Justification 5 x + 5 y = 20 + 3 x Distributive property -5 x Eliminating x from one side by subtracting. Combine like terms. - 5 x 5 y = -2 x + 20 5/5 y = -2/5 x + 20/5 Y = -2/5 x + 4 Eliminating the coefficient of y by dividing Divide and reduce fractions.

Example 9: 3 y – 21 = 12 x Procedure +21 3 y = 12 x + 21 3/3 y = 12/3 x + 21/3 Y = 4 x + 7 Justification +21 Eliminating constants from one side by adding. Combine like terms. Eliminating the coefficient of y by dividing Divide.

Example 10: 2 x + 3 y = 3 Procedure - 2 x Justification -2 x 3 y = -2 x + 3 3/3 y = -2/3 x + 3/3 Y = -2/3 x + 1 Eliminating x from one side by subtracting. Combine like terms. Eliminating the coefficient of y by dividing Divide and reduce fractions.

Example 11: x – 2 y = 4 Procedure -x Justification -x -2 y = -x + 4 -2/-2 y = -/-2 x + 4/-2 Y = 1/2 x - 2 Eliminating x from one side by subtracting. Combine like terms. Eliminating the coefficient of y by dividing Divide and reduce fractions.

Example 12: -2 x – y = - 3 Procedure + 2 x Justification +2 x -y = 2 x – 3 -1/-1 y = 2/-1 x – 3/-1 Y = -2 x + 3 Eliminating x from one side by adding. Combine like terms. Eliminating the coefficient of y by dividing Divide.