Question

1) x - 2y = 5, x² - y² = 8

2) x - y = 0, x² + xy - y² = 4
3) 3x + 4y = - 5, 2x² - xy + 5y² = 26
Pls it is simultaneous equations

Answer 1

To solve the given set of simultaneous equations, we can use the substitution method. We need to solve each equation for one variable, then substitute the value obtained into the other equation and solve it. Repeat this process for the other set of equations to find the values of x and y.

Step-by-step explanation:

The given set of equations are:

1) x - 2y = 5, x² - y² = 8

2) x - y = 0, x² + xy - y² = 4

3) 3x + 4y = -5, 2x² - xy + 5y² = 26

To solve these equations simultaneously, we can use substitution or elimination method. Let's solve the equations using the substitution method:

1. Solve the first equation for x: x = 2y + 5
2. Substitute this value of x in the second equation: (2y + 5)² - y² = 8
3. Simplify this equation: 4y² + 20y + 25 - y² = 8
4. Combine like terms: 3y² + 20y + 17 = 0
5. Now, solve this quadratic equation for y using factoring or the quadratic formula.
6. Once you find the value of y, substitute it back into the first equation to find the value of x.
7. Repeat the same steps for the other set of equations to find the values of x and y.