Question

1. What is the solution to the system of equations?

3x + 4y = 12
x + 2y = 10
(a) Show how to solve the system of equations using the linear combination or elimination method.
(b) Show that you can get the same answer by using the substitution method.


Please help worth 93 points

Answer 1

Explanation:

(1) 3x + 4y = 12

(2) x + 2y = 10

(2)*3: 3x+6y=30

by elimination (2)*3 - (1)

6y-4y=30-12

2y=18

y=9

x+2(9)=10

x=-8

rearrange (2): x=10-2y

substitute in (1): 3(10-2y)+4y=12

30-6y+4y=12

2y=30-12

y=9

x=10-2(9)

=-8

same ans either way

Answer 2

Explanation:

(a) In order to use the elimination method, multiply the second equation by 2.

It becomes 2x + 4y = 20.

Subtract that from the first equation: 3x + 4y = 12

3x + 4y - 2x - 4y = 12 - 20

x = -8

Put that back in the second equation: -8 + 2y = 10

2y = 18

y = 9

(b) In order to use the substitution method, subtract 2y from the second equation.

It becomes x + 2y - 2y = 10 - 2y

x = 10 - 2y

Substitute that into the first equation:

3(10 - 2y) + 4y = 12

30 - 6y + 4y = 12

30 - 2y = 12

2y = 18

y = 9

Put back into the equation for x:

x = 10 - 2(9)

= 10 - 18

= -8