Answer:
(-2, 7) and (0, 3)
Step-by-step explanation:
A graph of the two equations clearly shows the points of intersection.
The equations are conveniently graphed by a graphing calculator (as here) or by a spreadsheet program, on-line graphing tool, or graphing app.
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Alternate solution
You can set the two values of y equal to each other, then solve for x.
3x^2 +4x +3 = -2x +3
3x^2 +6x = 0 . . . . . subtract the right side expression
3(x)(x +2) = 0 . . . . . factor the equation
x = 0, x = -2 . . . . . . solutions that make the factors zero
y = -2{0, -2} +3 . . . . substitute the values of x into the expression for y
y = {0, 4} +3
y = {3, 7} . . . . . . . . . the values of y corresponding to x = {0, -2}
Then the points of intersection are (0, 3) and (-2, 7).
