Photo AI

Solve algebraically - OCR - GCSE Maths - Question 20 - 2021 - Paper 1

Question 20

Solve algebraically. y = x + 3 (x - 3)^2 + y^2 = 50 You must show your working.

Worked Solution & Example Answer:Solve algebraically - OCR - GCSE Maths - Question 20 - 2021 - Paper 1

Step 1

Substituting for y

96%

114 rated

Answer

Start by substituting the expression for y into the second equation. We know that:

$y = x + 3$

Substituting this into the equation:

$(x - 3)^2 + (x + 3)^2 = 50$

Step 2

Expanding the equation

99%

104 rated

Answer

Next, expand both squares:

$(x - 3)^2 = x^2 - 6x + 9$

$(x + 3)^2 = x^2 + 6x + 9$

Putting it all together, we have:

$x^2 - 6x + 9 + x^2 + 6x + 9 = 50$

Step 3

Combining like terms

96%

101 rated

Answer

Combine the like terms:

$2x^2 + 18 = 50$

Now, subtract 50 from both sides:

$2x^2 + 18 - 50 = 0$

This simplifies to:

$2x^2 - 32 = 0$

Step 4

Solving for x

98%

120 rated

Answer

Now, isolate the x^2 term:

$2x^2 = 32$

Divide by 2:

$x^2 = 16$

Taking the square root gives:

$x = 4 ext{ or } x = -4$

Step 5

Finding corresponding y values

97%

117 rated

Answer

Using the values of x to find y:

For $x = 4$ , we have:

$y = 4 + 3 = 7$

For $x = -4$ , we have:

$y = -4 + 3 = -1$

Thus, the solutions are:

$x = 4, y = 7$ $x = -4, y = -1$

Join the GCSE students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;