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22 Find the coordinates of the point where the line 4x+y=9 intersects the curve y+x^(2)=5. You must show all your working.

2222 Find the coordinates of the point where the line 4x+y=9 4 x+y=9 intersects the curve y+x2=5 y+x^{2}=5 . You must show all your working.

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Q. 2222 Find the coordinates of the point where the line 4x+y=9 4 x+y=9 intersects the curve y+x2=5 y+x^{2}=5 . You must show all your working.
  1. Solve linear equation for y: Solve the linear equation for yy.y=9−4xy = 9 - 4x
  2. Substitute expression into curve equation: Substitute the expression for yy into the curve equation.$9−4x\$9 - 4x + x^22 = 55\)
  3. Rearrange to form quadratic equation: Rearrange the equation to form a quadratic equation. x2−4x+9=5x^2 - 4x + 9 = 5
  4. Set quadratic equation to zero: Subtract 55 from both sides to set the quadratic equation to zero.\newlinex2−4x+4=0x^2 - 4x + 4 = 0

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