Answer:
Part 1) The solution of the system of equations is (2,-5)
Part 2) The solution of the system of equations is (2,4)
Step-by-step explanation:
Part 1) Linear combination
we have
[tex]3x+2y=-4[/tex] -----> equation A
[tex]4x-y=13[/tex] -----> equation B
Multiply equation B by 2 both sides
[tex]2(4x-y)=2*13[/tex]
[tex]8x-2y=26[/tex] -----> equation C
Adds equation A and equation C
[tex]3x+2y=-4\\8x-2y=26\\-------\\3x+8x=-4+26\\11x=22\\x=2[/tex]
Find the value of y
[tex]3(2)+2y=-4[/tex]
[tex]2y=-4-6[/tex]
[tex]2y=-10[/tex]
[tex]y=-5[/tex]
The solution of the system of equations is (2,-5)
Part 2) By graph
[tex]y=(1/2)x+3[/tex] -----> equation A
[tex]-3x+y=-2[/tex] -----> equation B
we know that
The solution of the system of equations is the intersection point both graphs
Using a graphing tool
The intersection point is (2,4)
therefore
The solution of the system of equations is the point (2,4)
see the attached figure
