Question

If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to y from the first equation is substituted into the second equation.

15x - y = -6
5x - 3y = -13

Answer 1

hellppp!

Answer 2

@Compassionate

Answer 3

@RadEn

Answer 4

15x - y = -6 --- subtract 15x from both sides
-y = -15x - 6 ---multiply by -1 to make x positive
y = 15x + 6

now you would sub 15x + 6 in for y in the other equation

Answer 5

ok so, 5x - 3 * 15x + 6 = -13

Answer 6

5x - 3y = -13
5x - 3(15x + 6) = -13

Answer 7

You need to put parenthesis....that way you know to distribute the -3 through the entire parenthesis

Answer 8

understand ? Do you have any questions ?

Answer 9

so i got this 5x - 45x + 18 = 13

Answer 10

check again....remember you are multiplying everything in the parenthesis by a -3. And don't forget that your 13 is negative.

Answer 11

oh haha, ok let me work this out on paper, my head isnt kinda foggy atm

Answer 12

40x = 5 is what i came out with?

Answer 13

ok i got the answer, thanks so much.

Answer 14

Solve the following system of equations.

x + 3y - z = 2
x - 2y + 3z = 7
x + 2y - 5z = -21

(2, 3, 5)

(-2, 3, 5)

(2, -3, 5)

(2, 3, -5)

Answer 15

is there a formula to solve this.

Answer 16

5x - 3(15x + 6) = -13
5x - 45x - 18 = -13 --- add 18 to both sides
5x - 45x = -13 + 18 -- combine like terms
-40x = 5 -- divid by -40
x = 5/-40
x = -1/8
now you would sub -1/8 in for x in either equation to find y

Answer 17

you would have to use elimination or substitution to solve a system of equations with 3 variables. I myself, prefer elimination. But thats just me.

Answer 18

The answer to the first problem was asking what the equation would look like so it was : 5x - 3(15x + 6) = -13

Answer 19

yes...that is correct

Answer 20

so could you set me up with the first step in the 3 equations to find it, they are horrid in my brain, as i have ADD.

Answer 21

?

Answer 22

this can be a little hard to understand.....you take 2 equations, any two.
x + 3y - z = 2 --->(-1)
x - 2y + 3z = 7
---------------
-x - 3y + z = -2 (result of multiplying by -1)
x - 2y + 3z = 7
--------------add
-5y + 4z = 5

now take one of the equations you used and the equation you did not use, and eliminate what you eliminated in the first part of the problem

x - 2y + 3z = 7 --->(-1)
x + 2y - 5z = -21
-----------------
-x + 2y - 3z = -7 (result of multiplying by -1)
x + 2y - 5z = -21
-----------------add
4y - 8z = -28

now take your results..
-5y + 4z = 5 --->(2)
4y - 8z = -28
---------------
-10y + 8z = 10 (result of multiplying by 2)
4y - 8z = -28
--------------add
-6y = - 18
y = -18/-6
y = 3

now sub 3 in for y in the equation that x was eliminated from
-5y + 4z = 5
-5(3) + 4z = 5
-15 + 4z = 5
4z = 5 + 15
4z = 20
z = 5

now sub 3 in for y and 5 in for z in any original equation
x + 3y - z = 2
x + 3(3) - 5 = 2
x + 9 - 5 = 2
x + 4 = 2
x = 2 - 4
x = -2

check...
x - 2y + 3z = 7
-2 - 2(3) + 3(5) = 7
-2 - 6 + 15 = 7
-8 + 15 = 7
7 = 7 (correct)

solution is (-2,3,5)