Mathematics·Algebra · NSSCO 6.3
Simultaneous equations
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Two equations, two unknowns, and one special pair of numbers that fits both at the same time — that is the whole idea of simultaneous equations. This lesson teaches all three methods slowly and side by side: elimination (add or subtract to make a letter vanish, multiplying first when the coefficients don't match), substitution (get one letter alone and slot it into the other equation), and the graphical method (draw both lines and read off where they cross). We form two equations from a word problem, and we always, always check the pair in both equations.
What you'll learn in this lesson
By the end you should be able to (NSSCO Mathematics 6.3):
- Understand that simultaneous equations have one pair of values (x, y) that satisfies both equations at the same time
- Solve two linear simultaneous equations by elimination — subtracting when matching terms have the same sign, adding when they have opposite signs
- Multiply an equation through first to match coefficients before eliminating
- Solve two linear simultaneous equations by substitution, rearranging one equation for a letter when needed
- Solve simultaneous equations graphically by drawing both lines and reading off the intersection point
- Form and solve a pair of simultaneous equations from a word problem
- Check a solution by substituting the pair back into both original equations
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Miss Jay Jay and Mike talk through the whole topic — with the figure and working drawn live.