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Solve the simultaneous equations 5x + y = 21 x - 3y = 9 x = ______________ y = ______________ - Edexcel - GCSE Maths - Question 7 - 2018 - Paper 1

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Question 7

Solve-the-simultaneous-equations--5x-+-y-=-21-x---3y-=-9--x-=-______________-y-=-______________-Edexcel-GCSE Maths-Question 7-2018-Paper 1.png

Solve the simultaneous equations 5x + y = 21 x - 3y = 9 x = ______________ y = ______________

Worked Solution & Example Answer:Solve the simultaneous equations 5x + y = 21 x - 3y = 9 x = ______________ y = ______________ - Edexcel - GCSE Maths - Question 7 - 2018 - Paper 1

Step 1

Step 1: Solve for y in the first equation

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Answer

From the equation (5x + y = 21), we can express (y) in terms of (x):

[ y = 21 - 5x ]

Step 2

Step 2: Substitute y in the second equation

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Answer

Substituting (y) in (x - 3y = 9):

[ x - 3(21 - 5x) = 9 ]

Expanding this gives:

[ x - 63 + 15x = 9 ]

Combining like terms:

[ 16x - 63 = 9 ]

Adding 63 to both sides:

[ 16x = 72 ]

Dividing by 16:

[ x = \frac{72}{16} = 4.5 ]

Step 3

Step 3: Find y using the value of x

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Answer

Substituting (x = 4.5) back into the equation for (y):

[ y = 21 - 5(4.5) ]

Calculating gives:

[ y = 21 - 22.5 = -1.5 ]

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