How Do I Know What to Multiply By When Solving Systems of Equations?
- 1). Solve the linear system 2x + 6y = 10 and 4x + 2y = 15. Look for ways you can multiply one equation to eliminate the variable of the other equation during addition: -2 * (2x + 6y = 10) and -3 * (4x + 2y = 15) will both work. Use the easier of the two (the -2 method) to eliminate the first variable.
- 2). Multiply (2x + 6y = 10) by -2: -4x + -12y = -20. Add the terms to the like terms from the second equation: -4x + 4x = 0, -12y + 2y = -10y and - 20 + 15 = -5. Write the answers as an equation: -10y = - 5. Divide both sides by -10 to solve for y: y = 5/10 or 1/2 or 0.5.
- 3). Plug the value y = 0.5 back into one of the original equations: 2x + 6(0.5) = 10 or 2x + 3 = 10. Subtract 3 from both sides: 2x = 7. Divide both sides by 2 to find x: x = 7/2 or x = 3.5. Write the final answer as (3.5, 0.5).
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