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Solve the simultaneous equations - OCR - GCSE Maths - Question 21 - 2020 - Paper 1

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Solve the simultaneous equations. 2x + 3y = 10. 3x + 5y = 17. x = .................................................... y = ........................................... show full transcript

Worked Solution & Example Answer:Solve the simultaneous equations - OCR - GCSE Maths - Question 21 - 2020 - Paper 1

Step 1

2x + 3y = 10

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Answer

To solve the first equation for x, we can express it in terms of y:

  1. Rearrange the equation:

    2x=10−3y2x = 10 - 3y

  2. Divide both sides by 2 to solve for x:

    x=10−3y2x = \frac{10 - 3y}{2}

Step 2

3x + 5y = 17

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Answer

Next, substitute the expression for x from the first equation into the second equation:

  1. Substitute x=10−3y2x = \frac{10 - 3y}{2} into the second equation:

    3(10−3y2)+5y=173\left(\frac{10 - 3y}{2}\right) + 5y = 17

  2. Multiply through by 2 to eliminate the fraction:

    3(10−3y)+10y=343(10 - 3y) + 10y = 34

  3. Distribute 3:

    30−9y+10y=3430 - 9y + 10y = 34

  4. Combine like terms:

    30+y=3430 + y = 34

  5. Solve for y:

    y=34−30=4y = 34 - 30 = 4

Step 3

Find x using y = 4

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Answer

Now that we have found y, substitute it back into the equation for x:

  1. Substitute y=4y = 4 into the equation:

    x=10−3(4)2x = \frac{10 - 3(4)}{2}

  2. Calculate:

    x=10−122=−22=−1x = \frac{10 - 12}{2} = \frac{-2}{2} = -1

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