How to Solve Algebraic Equations by Addition

Solving Equations with One Variable

• 1

  Examine the addition equation, 5x + 15 = 30. The term 5x has a variable and a coefficient, meaning that the value of x is multiplied by five. 15 is positive and is added to the equation and together the product of 5 and x plus 15 should equal 30. Use the inverse operations to move terms.

• 2

  Subtract 15 from both sides of the equation to keep the sides of the equation equal to each other and balanced. 5x + 15 -- 15 = 30 -- 15. Simplify the equation, 5x = 15.

• 3

  Divide both sides of the equation by 5 to get x by itself and set equal to a value. 5x ÷ 5 = 15 ÷ 5. Simplify the equation x = 3.

• 4

  Plug the value of 3 back in wherever there is an x, 5(3) + 15 = 30 and simplify, 15 + 15 = 30.

• 5

  Examine the equation 2x + 3 = 7 + x. The product of two and x plus three should equal the sum of seven and x.

• 6

  Move the lowest variable from one side of the equation to the other, 2x -- x + 3 = 7 + x -- x. Simplify, x + 3 = 7. Move 3 to the other side of the equation and simplify, x + 3 -- 3 = 7 -- 3 = x = 4.

• 7

  Plug the value of four back into the equation, 2(4) + 3 = 7 + 4. Simplify, 8 + 3 = 7 + 4, to which both sums are 11.

Solving Equation with Two Variables

• 8

  Examine the equations 2x + y = 4 and 4x + 3y = 10. Now you must solve for both variables to check for accuracy.

• 9

  Pick one variable to isolate. Since y is already by itself in the first equation, this will be the easier one. Subtract 2x to the other side of the equation, y = 4 -- 2x.

• 10

  Substitute the value of y back into the second equation, 4x + 3(4 -- 2x) = 10. This is called the substitution method and is commonly used to find intercepts for graphing.

• 11

  Solve for the parentheses by multiplying each inside term by the outside term, 3 x 4 = 12 and 3 x -2x = -6x. Simplify the equation, 4x + 12 -- 6x = 10.

• 12

  Combine like terms and simplify, 4x -- 6x = -2x + 12 = 10. Move 12 to the other side and simplify, -2x = -2.

• 13

  Divide both sides by -2 and simplify, x = 1.

• 14

  Plug the value of x back into the simplest formula, which is the formula for y, y = 4 -- 2(1). Simplify for the value of y = 4 -- 2 = y = 2.

• 15

  Plug the values of x and y back into any formula to check, 4(1) + 3(2) = 10. Simplify for 4 + 6 = 10, which is true.