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.

worth 93 points

Step-by-step 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

22 and 22

step-by-step explanation:

10 plus 12 equals 22.

12 plus 10 also equals 22 because regardless of what order they're in, they're gonna equal the same thing.

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.