Question

Solve for the simultaneous equation
X^2 + y - 5=0
Y - 7x + 3= 0

Answer 1

To solve the simultaneous equations:

1) X^2 + y - 5 = 0
2) y - 7x + 3 = 0

We can solve this system of equations by substitution. First, solve equation (2) for y:

y = 7x - 3

Now, substitute this value of y into equation (1):

x^2 + (7x - 3) - 5 = 0

Rearrange this equation to simplify:

x^2 + 7x - 8 = 0

Now, we can solve this quadratic equation by factoring or using the quadratic formula. In this case, the quadratic equation factors as:

(x + 8)(x - 1) = 0

Setting each factor equal to zero:

x + 8 = 0 --> x = -8
x - 1 = 0 --> x = 1

So, we have two possible x-values, x = -8 and x = 1. Now, substitute these values into equation (2) to solve for the corresponding y-values:

For x = -8:
y = 7(-8) - 3 = -56 - 3 = -59

For x = 1:
y = 7(1) - 3 = 7 - 3 = 4

Therefore, the solutions to the simultaneous equations are x = -8, y = -59 and x = 1, y = 4.