Question

Match the systems of equations with their solution sets. Tiles y + 12 = x2 + x x + y = 3 y − 15 = x2 + 4x x − y = 1 y + 5 = x2 − 3x 2x + y = 1 y − 6 = x2 − 3x x + 2y = 2 y − 17 = x2 − 9x -x + y = 1 y − 15 = -x2 + 4x x + y = 1 Pairs Solution SetLinear-Quadratic System of Equations {(-2, 3), (7, -6)} arrowBoth {(-5, 8), (3, 0)} arrowBoth {(-2, 5), (3, -5)} arrowBoth {(2, 3), (8, 9)} arrowBoth

Answer 1

We know that
the solution of the systems of equations is the intersection both graphs

case 1)
$y+12= x^{2} +x \\ x+3=y$

using a graph tool
see the attached figure N 1

the solution is the set {(-5, 8), (3, 0)}

case 2)
$y-15= x^{2} +4x \\ x-y=1$

using a graph tool
see the attached figure N 2

the solution is the set------> there is no solution

case 3)
$y+5= x^{2} -3x \\ 2x+y=1$
using a graph tool
see the attached figure N 3

the solution is the set {(-2, 5), (3, -5)} 

case 4)
$y-6= x^{2} -3x \\ x+2y=2$
using a graph tool
see the attached figure N 4

the solution is the set -----> there is no solution

case 5)
$y-17= x^{2} -9x \\ -x+y=1$
using a graph tool
see the attached figure N 5

the solution is the set {(2, 3), (8, 9)}

case 6)
$y-15=- x^{2} +4x \\ x+y=1$
using a graph tool
see the attached figure N 6

the solution is the set {(-2, 3), (7, -6)}