Question

Solve the simultaneous equations
a. x=4-y
b. y² = 3x 19

Answer 1

The equations x = 4 - y and y² = 3x can be solved by substituting x from the first equation into the second, resulting in a quadratic equation that can be factored. The solutions are x = 8, y = -4 and x = 1, y = 3.

Step-by-step explanation:

Let's solve the given simultaneous equations:

1. x = 4 - y (Equation a)

2. y² = 3x (Equation b)

We can substitute the expression for x from equation a into equation b:

y² = 3(4 - y)

Expanding and rearranging the equation:

y² = 12 - 3y

Moving all terms to one side:

y² + 3y - 12 = 0

This is a quadratic equation, which can be factored to:

(y + 4)(y - 3) = 0

So the solutions for y are:

• y = -4
• y = 3

Substituting these values back into equation a:

• For y = -4:
• x = 4 - (-4) = 8
• For y = 3:
• x = 4 - 3 = 1

Therefore, we have two sets of solutions for the simultaneous equations:

• Solution 1: x = 8, y = -4
• Solution 2: x = 1, y = 3