A-Level Edexcel Maths Pure Graphs of Functions: Solve the simultaneous equations

Solve the simultaneous equations $$ x + y = 2 $$ $$ x^2 + 2y = 12 - Edexcel - A-Level Maths Pure - Question 6 - 2005 - Paper 2

Question 6

Solve the simultaneous equations $$ x + y = 2 $$ $$ x^2 + 2y = 12. $$

Worked Solution & Example Answer:Solve the simultaneous equations $$ x + y = 2 $$ $$ x^2 + 2y = 12 - Edexcel - A-Level Maths Pure - Question 6 - 2005 - Paper 2

Step 1

1. Rearranging the First Equation

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Answer

From the first equation, we can express y in terms of x:

y = 2 - x

Step 2

2. Substituting in the Second Equation

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Answer

Next, substitute this expression for y into the second equation:

x^2 + 2(2 - x) = 12

Step 3

3. Simplifying the Equation

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Answer

Expanding the equation:

x^2 + 4 - 2x = 12

Then, rearranging gives:

x^2 - 2x - 8 = 0

Step 4

4. Factoring the Quadratic Equation

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Answer

Now, we factor the quadratic:

(x - 4)(x + 2) = 0

Step 5

5. Finding x Values

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Answer

Setting each factor to zero gives:

x - 4 = 0 ightarrow x = 4

x + 2 = 0 ightarrow x = -2

Step 6

6. Finding Corresponding y Values

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Answer

Now, substitute these x values back into the equation for y:

For $x = 4$ :

y = 2 - 4 = -2

Thus, one solution is (4, -2).

For $x = -2$ :

y = 2 - (-2) = 4

Thus, another solution is (-2, 4).

Solve the simultaneous equations $$ x + y = 2 $$ $$ x^2 + 2y = 12 - Edexcel - A-Level Maths Pure - Question 6 - 2005 - Paper 2

Worked Solution & Example Answer:Solve the simultaneous equations $$ x + y = 2 $$ $$ x^2 + 2y = 12 - Edexcel - A-Level Maths Pure - Question 6 - 2005 - Paper 2

1. Rearranging the First Equation

2. Substituting in the Second Equation

3. Simplifying the Equation

4. Factoring the Quadratic Equation

5. Finding x Values

6. Finding Corresponding y Values

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