Question

Help and explain too (using elimination to solve systems of equations ) !!!!!

Answer 1

x=3 y=5

Explanation:

it's simultaneous equations so you first try matching the x or the y on both equations

on the first equation the ys are matching so:

4x+y=17

2x+y=11

2x=6

x=3

now that you have x you substitute it back into the equation to get y

6+y=11

-6 -6

y=5

Answer 2

(3,5)

(3,2)

(7,0)

(8,1)

Explanation:

1.)

Subtract the two equations

(4x+y)-(2x+y)=17-11

2x=6

x=3

plug this into the first equation

4(3)+y=17

y=5

2.) we need one set of the same variable's coefficents to match (so that when we add/subtract the two equations a variable cancels out). To do this multiply the first equation by 1.5

1.5(3x+2y)=13*1.5

4.5x+3y=19.5

Subtract the second equation

(4.5x+3y)-(2x+3y)=19.5-12

2.5x=7.5

x=3

plug this into the first equation

3(3)+2y=13

2y=4

y=2

3.)

Mulitply the first equation by 3

3(x-2y)=7*3

3x-6y=21

subtract this and the second equation

(3x-6y)-(3x+y)=21-21

-7y=0

y=0

plug this into the first equation

x-2(0)=7

x=7

3.)

add the two equations

(x+5y)+(x-5y)=13+3

2x=16

x=8

plug this into the first equation

8+5y=13

5y=5

y=1