Question

1). Linear Combination (SHOW WORK)

3x +2y = −4

4x − y= 13


2). graph

y= 1/2 x + 3

-3x+y=-2

Answer 1

Part 1) The solution of the system of equations is (2,-5)

Part 2) The solution of the system of equations is (2,4)

Explanation:

Part 1) Linear combination

we have

`3x+2y=-4` -----> equation A

`4x-y=13` -----> equation B

Multiply equation B by 2 both sides

`2(4x-y)=2*13`

`8x-2y=26` -----> equation C

Adds equation A and equation C

`3x+2y=-4\\8x-2y=26\\-------\\3x+8x=-4+26\\11x=22\\x=2`

Find the value of y

`3(2)+2y=-4`

`2y=-4-6`

`2y=-10`

`y=-5`

The solution of the system of equations is (2,-5)

Part 2) By graph

`y=(1/2)x+3` -----> equation A

`-3x+y=-2` -----> 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