Question

A system of equations is shown. y = 3x - 2;. y = x^2. What are the solutions to the system of equations?

Answer 1

Answer: the solutions to the system of equations are x = 2 and x = 1

Explanation:

The system of equations given equation is

y = 3x - 2 - - - - - - - - - - 1

y = x^2 - - - - - - - - - - - - 2

Substituting 1 into equation 2, it becomes

x^2 = 3x - 2

x^2 - 3x + 2 = 0

We would apply the method of factorization in solving the equation. We will get two numbers such that when added, the result would be - 3x and when multiplied, the result would be 2x^2. The numbers are - 2x and - x. It becomes

x^2 - 2x - x + 2 = 0

x(x - 2) - 1(x - 2) = 0

(x - 2)(x - 1) = 0

x - 2 = 0 or x - 1 = 0

x = 2 or x = 1

.

Answer 2

(1,1) and (2,4) are the solutions to the system of equations.

Explanation:

The two equations are:

`y=x^(2)`---------1

`y=3x-2`---------2

Putting value of y from equation 1 in equation 2 we get:

`x^(2)=3x-2\\x^(2)-3x+2=0\\Factorising\\x^(2)-x-2x+2=0\\x(x-1)-2(x-1)=0\\(x-1)(x-2)=0\\x=1,x=2`

When x=1 :
`y=x^(2)=1`

When x=2
`y=x^(2) =4`

The solutions are (1,1) and (2,4).