How to solve this maths question simultaneously

y=x^2 and y=5x-6

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It's best to use substitution here. Both equations are equal to y so

x^2 = 5x - 6

Rearrange to 0

x^2 - 5x + 6 = 0

Solve by factorising

(x-3)(x-2) = 0

x = 3 or 2

When x=3, y=5 x 3 - 6 = 9

When x=2, y=5 x 2 - 6 = 4

substitute the first y value into the second equation

gives

x^2 = 5x - 6
x^2 - 5x + 6 = 0

factorise

[x-3][x-2] = 0

x = +3 or + 2

two values of x produces two values for y

y = x^2

so when x = 2 y = 4 and when x = 3 y = 9

x^2 = 5x-6

x^2 - 5x + 6 = 0

x^2 - 3x -2x +6 = 0

x(x-3) -2(x-3) = 0

(x-2)(x-3) = 0

x = 2 or 3

y = 4 or 9

solutions : (2,4) or (3,9)

y= x^2 & y = 5x - 6
so x^2 = 5x- 6
or x^2 -5x + 6 =0
or x^2 - 3x -2x +6 =0
or x( x-3) - 2( x- 3 = 0
(x- 3 ) ( x-2 )=0
so x= 2 & 3 ans
so y = 4 & 9 ans

putting the value of y in 2nd x^2=5x-6 x^2-5x+6=0 (x-3)(x-2)=0 x=3 or x=2 so y=9 or 4

(3,9),(2,4)

x ² = 5x - 6
x ² - 5x + 6 = 0
(x - 3)(x - 2) = 0
x = 3 , x = 2
y = 9 , y = 4