Question

Explain, in complete sentences, how you would use the substitution method to solve the following system of equations. Provide the solution to the system.

14x - y = -10
7x + 2y = 15

Answer 1

Look at your first equation....we want to get y by itself.

14x - y = -10 --- add y to both sides
14x = -10 + y -- add 10 to both sides
14x + 10 = y

now sub 14x + 10 in for y in the other equation
7x + 2y = 15
7x + 2(14x + 10) = 15 --- distribute through the parenthesis
7x + 28x + 20 = 15 -- subtract 20 from both sides
7x + 28x = 15 - 20 -- combine like terms
35x = -5 -- divide both sides by 35
x = -5/35
x = - 1/7

now sub -1/7 in for x in either equation to find y
14x - y = -10
14(-1/7) - y = -10
-14/7 - y = -10
-2 - y = -10
-y = -10 + 2
-y = -8
y = 8

check...
7x + 2y = 15
7(-1/7) + 2(8) = 15
-1 + 16 = 15
15 = 15 (correct)

x = -1/7 and y = 8

any questions ?

Answer 2

14x - y = -10
7x + 2y = 15

let x=(n/14 -5/14)
let y=(n+5)

and substitute

14(n/14 - 5/14) - (n+5) = -10
7(n/14 - 5/14) + 2(n+5) = 15


n - 5 -n -5 = -10
n/2 - 5/2 + 2n +10 = 15


- 5-5 = -10 ; always true
5n/2 - 15/2 = 15; solve for n

Answer 3

prolly typoed somethign in there :)

Answer 4

@texaschic101 Thank You for explaining. It really helped

Answer 5

I am always glad to help :)