How Do You Solve Systems Using Linear Combinations?
• Move all terms with variables to one side. Terms without exponents can go on the opposite side. 3x = 2y + 7 → 3x – 2y = 7 4y = 10 – 2x → 2x + 4y = 10 • Choose a variable to eliminate first. In this example, y will be eliminated. • Multiply the equations so that there is the same number of that variable in both equations. Find the least common multiple (LCM) of the coefficients of the variable you chose to eliminate. Multiply the equations accordingly so that both of the coefficients are of the same value, except one is negative. LCM of 2 and 4 is 4. (3x – 2y = 7) × 2 → 6x – 4y = 14 (2x + 4y = 10) × 1 → 2x + 4y = 10 • Add the equations. Add each of the terms together just as if you were adding 214 and 631. 6x – 4y = 14 2x + 4y = 10 8x + 0 = 24 • Solve for the remaining variable. This can be done using any methods to solve for a one-variable equation. 8x + 0 = 24 8x = 24 (8x) / 8 = 24 / 8 x = 3 • Solve for the eliminated variable. Go back to any of the previous equations during your wo
