Question

Solve These Simultaneous Equations:
x squared + y squared = 1
x + 2y =1

Answer 1

To solve for x and y in the simultaneous equations x squared + y squared = 1 and x + 2y = 1, we isolate x in the second equation and substitute it into the first equation. This leads to two possible solutions for y, which then give us two corresponding x values, resulting in two solution pairs for the equations.

Step-by-step explanation:

To solve these simultaneous equations, we need to find values of x and y that satisfy both equations:

• x squared + y squared = 1
• x + 2y = 1

Let's solve the second equation for x:

x = 1 - 2y

Now, substitute this x value into the first equation:

(1 - 2y)2 + y2 = 1

Expand and simplify:

1 - 4y + 4y2 + y2 = 1

Combine like terms and move all terms to one side:

5y2 - 4y = 0

Factoring out y:

y(5y - 4) = 0

This gives two possible values for y:

1. y = 0
2. y = 4/5

For y = 0, substituting back into x + 2y = 1:

x = 1

For y = 4/5, substituting back into x + 2y = 1:

x = 1 - 2(4/5)

x = 1 - 8/5

x = -3/5

The solutions to the simultaneous equations are (1, 0) and (-3/5, 4/5).