Systems of equations are used when multiple conditions must be met at the same time. In business, they help determine the break-even point where costs equal revenue. In physics, they predict when and where two moving objects will collide.
When you have two unknown values (like x and y), you need two equations to find their exact values. By combining the equations, we can eliminate one unknown and solve the puzzle.
When subtracting equations in the elimination method, many people forget to flip the sign of EVERY term in the second equation. Always double-check your signs when subtracting!
Solve the following systems of equations.
Did you know? The ancient Chinese text 'The Nine Chapters on the Mathematical Art' (around 150 BC) features the first known use of solving systems of linear equations using a method very similar to modern matrices!