Linear Simultaneous Equations - Substitution (AQA A-Level Mathematics): Quizzes

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Linear Simultaneous Equations - Substitution
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What does the substitution method involve?

Rearranging one equation, then substituting

When substituting x=y−5x = y - 5 into x2+y2=9x^2 + y^2 = 9, what is the first step?

Replace xx with y−5y - 5

After substituting in the first example, which equation is formed?

2y2−10y+16=02y^2 - 10y + 16 = 0

What are the solutions for yy in the first example?

y=7y = 7 or y=4y = 4

If y=7y = 7 and x=y−5x = y - 5, what is xx?

x=2x = 2

What are the solution pairs for the first example?

(2,7)(2, 7) and (−1,4)(-1, 4)

In Example 2, after substitution, which equation forms?

4x2+4x+1=04x^2 + 4x + 1 = 0

What is the value of xx in Example 2?

x=−12x = -\frac{1}{2}

What does a single solution indicate about a line and curve?

The line is tangent to the curve

What is a tangent to a curve?

A line that touches without cutting it

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