Question

Solve the system.

y= 3x^2−2x+3​

y = x + 3


The solutions are (__,__) and (__,__).

Answer 1

the solutions are (1,4) and (0,3)

Explanation:

step 1: Subtract the equations

step 2: refine

step 3:Plug the solutionsx=1,x=0 into y=3x^2-2x+3

step 4: verify

Answer 2

(0,3) and (1,4) are solution sets of given system

Explanation:

Given that:

y= 3x^2−2x+3​ ------------- eqA

y = x + 3 ------------------ eqB

Putting value of y from eqB to eqA

x + 3 = 3x^2−2x+3

Taking all variables to left side:​

Signs pf transferred terms will be changed

3x^2−2x+3​ - x - 3 = 0

Adding like terms we get:

3x^2−3x = 0

Dividing both sides by 3 we get:

x^2 - x = 0

Now take x common:

x(x-1)= 0

So

x = 0 and x = 1

Now put value in eqB

y = 0 + 3 and y= 1 + 3

we get:

y = 3 and y = 4

So solution sets are:

(0,3) and (1,4)

i hope it will help you!