simultaneous equation
x squared = 4-y
x = y+2
Express 3x squared + 2x + 1 in the form a(x+p)squared + q where a,p and q are real numbers
x^2 = 4-y and x = y+2
sub the 2nd into the first
(y+2)^2 = 4-y
y^2 + 4y + 4 = 4-y
y^2 + 5y = 0
y(y+5) = 0
y = 0 or y = -5
if y = 0 , then x = 4-0 = 4
if y = -5 , then x = 4-(-5) = 9
To solve the simultaneous equations:
1. Substitute the value of x from the second equation into the first equation:
x = y + 2
x^2 = 4 - y
(y + 2)^2 = 4 - y
2. Expand and simplify the equation:
(y^2 + 4y + 4) = 4 - y
3. Rearrange the equation to bring all terms to one side:
y^2 + 4y + y + 4 - 4 = 0
y^2 + 5y + 0 = 0
4. Factorize the equation if possible:
y(y + 5) = 0
5. Set each factor equal to zero and solve for y:
y = 0 or y + 5 = 0
If y = 0, substitute this back into the second equation to find x:
x = y + 2
x = 0 + 2
x = 2
If y + 5 = 0, then y = -5. Substitute this back into the second equation:
x = y + 2
x = -5 + 2
x = -3
Therefore, the solution to the simultaneous equations is:
x = 2, y = 0
or
x = -3, y = -5