One Linear, One Non-linear (Leaving Cert Mathematics): Quizzes

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One Linear, One Non-linear
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What key points should you consider in solving a pair of simultaneous equations?

One is linear, one is non-linear

What is the main goal when solving simultaneous equations with one linear and one non-linear?

Find their intersection points

How do you solve for xx in the pair: x+2y=8x + 2y = 8 and x2+y2=52x^2 + y^2 = 52?

Express xx as 8−2y8 - 2y and substitute

What is the first step to eliminate y from x+2y=8x + 2y=8?

Express x as 8−2y8-2y

How do you find xx after yy is known?

Plug yy into x=8−2yx=8-2y

What are the solutions (x,y)(x,y) for the system?

(−4,6)(-4,6) and (7.2,0.4)(7.2,0.4)

What is the intersection point of the circle and line in the diagram?

Two points of intersection

What do the diagrams in the note illustrate?

Points of intersection

What does solving simultaneous equations geometrically involve?

Finding intersection points

What is the purpose of substituting yy from first into second eq?

Reduce to one variable

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