Simultaneous Equations

Simultaneous Equations (Linear)

Equation 1:     2x + 3y  = 8 Equation 2:     3x + 2y  = 7 Step 1: Multiply each equation the first number in the opposite equation.    3 (2x + 3y = 8) --->    6x + 9y = 24   2 (3x + 2y = 7) --->    6x + 4y = 14        Both equations now have the same leading coefficient = 6   Step 2: Subtract the second equation from the first.           6x + 9y = 24           6x + 4y = 14                               5y  = 10                                  y = 2                  Step 3: Substitute y = 2 into either Equation 1 or Equation 2 above and solve for x. We'll use Equation 1.           2x + 3(2) = 8            2x + 6 = 8           Subtract 6 from both sides           2x = 2                  Divide both sides by 2           x = 1  Solution: x = 1, y = 2 or (1,2).