Question

Match the systems of equations to their solutions. Tiles 2x + y = 12 x = 9 − 2y x + 2y = 9 2x + 4y = 20 x + 3y = 16 2x − y = 11 y = 11 − 2x 4x − 3y = -13 y = 10 + x -3x + 3y = 30 2x + y = 11 x − 2y = -7 Pairs x = 2, y = 7 arrowBoth x = 5, y = 2 arrowBoth x = 3, y = 5 arrowBoth x = 7, y = 3 arrowBoth

Answer 1

we have
1) systems of equations 1
2x + y = 12
x = 9 − 2y
using a graph tool
see the attached figure
the solution is the point ------------> (5,2)

2) systems of equations 2
x + 2y = 9
2x + 4y = 20
using a graph tool
see the attached figure
the solution is the point -------> has no solution the two lines are parallel

3) systems of equations 3
x + 3y = 16
2x − y = 11
using a graph tool
see the attached figure
the solution is the point ------------> (7,3)

4) systems of equations 4
y = 11 − 2x
4x − 3y = -13
using a graph tool
see the attached figure
the solution is the point ------------> (2,7)

5) systems of equations 5
y = 10 + x -----------> multiplying by 3-----> 3y=30+3x------> -3x + 3y = 30
-3x + 3y = 30
equation 1 and equation 2 are equals--------> the system has no solution

6) systems of equations 6
2x + y = 11
x − 2y = -7
using a graph tool
see the attached figure
the solution is the point ------------> (3,5)