Solving Linear and Non-Linear Equations

What is the first step when solving simultaneous equations using the substitution method, especially when one equation is linear and the other is non-linear?

• Substitute the non-linear equation into the linear equation.

• Rearrange the linear equation to express one variable in terms of the other.

• Expand the non-linear equation.

• Factorize both equations.

Given the simultaneous equations x² + y² = 5 and 3y = x + 5, what is the result of rearranging the linear equation to let x be the subject?

• x = 3y + 5

• x = (3y + 5) / 3

• x = 3y - 5

• x = (3y - 5) / 3

After substituting the expression for x into the non-linear equation (x² + y² = 5) and expanding, what is the simplified quadratic equation in terms of y before setting it to zero?

• 9y² - 30y + 25 = 5

• 10y² - 30y + 25 = 5

• 10y² - 30y + 30 = 0

• 9y² + y² = 5

What is the factored form of the quadratic equation y² - 3y + 2 = 0?

• (y + 2)(y + 1)

• (y - 2)(y - 1)

• (y + 2)(y - 1)

• (y - 2)(y + 1)

Using the equation x = 3y - 5, what are the corresponding x-values for y = 2 and y = 1?

• x = 1 and x = -2

• x = 1 and x = 2

• x = -1 and x = -2

• x = -1 and x = 2