GCSE Edexcel Maths Simultaneous Equations: Solve algebraically the simultan

Solve algebraically the simultaneous equations x^{2} + y^{2} = 25 y - 3x = 13 (Total for Question 20 is 5 marks) - Edexcel - GCSE Maths - Question 20 - 2017 - Paper 1

Question 20

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Solve algebraically the simultaneous equations x^{2} + y^{2} = 25 y - 3x = 13 (Total for Question 20 is 5 marks)

Worked Solution & Example Answer:Solve algebraically the simultaneous equations x^{2} + y^{2} = 25 y - 3x = 13 (Total for Question 20 is 5 marks) - Edexcel - GCSE Maths - Question 20 - 2017 - Paper 1

Step 1

Substituting for $y$

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Answer

From the second equation, rearrange to find $y$ : $y = 3x + 13$ . Now substitute this expression for $y$ into the first equation.

Step 2

Expanding the first equation

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Answer

Substituting gives us: $x^{2} + (3x + 13)^{2} = 25$ . Expanding $(3x + 13)^{2}$ yields: $x^{2} + (9x^{2} + 78x + 169) = 25.$

Step 3

Combining like terms

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Answer

Combine the terms: $10x^{2} + 78x + 169 = 25$ . Subtract 25 from both sides to set the equation to zero: $10x^{2} + 78x + 144 = 0.$

Step 4

Factoring

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Answer

Now, factor the quadratic equation, if possible:

(5x + 12)(2x + 12) = 0.$$

Step 5

Finding the values of $x$

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Answer

Setting each factor to zero gives:

2x + 12 = 0.$$ This leads to $x = - rac{12}{5}$ and $x = -6$.

Step 6

Finding the corresponding $y$ values

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Answer

Substituting back into $y = 3x + 13$ :

For $x = - rac{12}{5}$ : $y = 3(- rac{12}{5}) + 13 = - rac{36}{5} + 13 = rac{29}{5}.$
For $x = -6$ : $y = 3(-6) + 13 = -18 + 13 = -5.$ Thus the solutions are: $(- rac{12}{5}, rac{29}{5})$ and $(-6, -5)$ .

Solve algebraically the simultaneous equations x^{2} + y^{2} = 25 y - 3x = 13 (Total for Question 20 is 5 marks) - Edexcel - GCSE Maths - Question 20 - 2017 - Paper 1

Worked Solution & Example Answer:Solve algebraically the simultaneous equations x^{2} + y^{2} = 25 y - 3x = 13 (Total for Question 20 is 5 marks) - Edexcel - GCSE Maths - Question 20 - 2017 - Paper 1

Substituting for $y$

Expanding the first equation

Combining like terms

Factoring

Finding the values of $x$

Finding the corresponding $y$ values

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