Question

Solve the simultaneous equation
y= х^2
у-5x +4=0

Answer 1

To solve the simultaneous equations, substitute the value of y in the second equation with the expression for y in the first equation. Factorize the quadratic equation to find the values of x. Substitute the values of x back into one of the equations to find the values of y.

Step-by-step explanation:

To solve the simultaneous equations:

1. Substitute the value of y in the second equation with the expression for y in the first equation:

(x^2 - 5x + 4) = 0

2. Factorize the quadratic equation to find the values of x:

(x - 1)(x - 4) = 0

x = 1 or x = 4

3. Substitute the values of x back into one of the equations to find the values of y:

If x = 1, then y = (1)^2 = 1

If x = 4, then y = (4)^2 = 16

The solutions to the simultaneous equations are x = 1, y = 1 and x = 4, y = 16.

Answer 2

To solve this system of simultaneous equations, we can start by substituting the first equation into the second equation to eliminate one of the variables.The first equation is y = x^2.

The second equation is y - 5x + 4 = 0.

If we substitute the first equation into the second equation, we get:

x^2 - 5x + 4 = 0We can then solve this quadratic equation using the quadratic formula:x = (-b +/- sqrt(b^2 - 4ac)) / (2a)Where a = 1, b = -5, and c = 4. Plugging these values into the formula, we get:

x = (5 +/- sqrt(25 - 16)) / 2

= (5 +/- sqrt(9)) / 2

= (5 +/- 3) / 2

= 8 / 2 or 2 / 2

= 4 or 1

These are the values of x that solve the system of equations. To find the corresponding values of y, we can substitute these values of x back into either of the original equations.If x = 4, then y = (4)^2 = 16.If x = 1, then y = (1)^2 = 1.

Therefore, the solutions to the system of equations are (4, 16) and (1, 1).