Solve by substitution. x-3y=4, -3x+5y=-14?

Question

Thanks

Answer 1

Change the first equation to x = 3y + 4, and subst. it into the second:

-3(3y + 4) + 5y = -14

-9y - 12 + 5y = -14

-4y = = -2

y = 1/2

x = 3(1/2) + 4 = 3/2 + 8/2 = 11/2

x= 11/2 and y = 1/2

that's it!

Answer 2

Solving by substitution meaning you need to solve one equation for one single variable and then plug what it equals in to the other.

Solve first one for x

x - 3y = 4 , add 3y to both sides

x = 3y + 4 , now that we know that x = 3y + 4 then put it in for x in the second location where ever you see x

-3x + 5y = -14 , make the substitution

-3 (3y +4) + 5y = -14 , distribute the -3

-9y - 12 + 5y = -14 , combine the y's and add 12 to both sides

-4y = -2 or y = 1/2 , then plug 1/2 in for y

x - 3(1/2) = 4 or x - 3/2 = 4

x = 11/2

Answer 3

First, solve for x in the first equation.
x - 3y = 4
x = 4 + 3y

Then substitute 4 + 3y in for x in the second equation and solve for y.
-3x + 5y = -14
-3(4 + 3y) + 5y = -14
-12 + -9y +5y = -14
-12 - 4y = -14
-4y = -2
y = 1/2

Finally, substitute this value for y into one of the original equations, and solve for x.
x - 3(1/2) = 4
x = 11/2

So: x = 11/2 and y = 1/2

Answer 4

from first equation
x-3y = 4
x = 4 + 3y
put the new value of x in second equation
-3(4+3y) + 5y = -14
-12 - 9y + 5y = -14
-9y + 5y = -14 + 12
-4y = -2
4y = 2
y = 2/4
y= 1/2
put new value of y in first equation
x - 3(1/2) = 4
x - 3/2 = 4
x = 4 + 3/2
x = 8/2 + 3/2
x = 11/2
therefor
x= 11/2 and
y = 1/2

Answer 5

x - 3y = 4 can be written as x = 4+3y by adding 3y to both sides of the equation.

now substitute the x in -3x+5y = -14 with x = 4+3y

you will get -3(4+3y) +5y = -14

at this point you have one equation and one unknown. solve for y then plug that answer into one of the original equations and solve for x. hopefully you can figure out the rest from here.

Answer 6

1st eqn:
x= 3y+4

-3x + 5y = -14
-3(3y+4) + 5y = -14
-9y - 12 + 5y = -14
-4y = -2

y = 1/2

x = 3y+4
x = 3(1/2) +4

x = 11/2
(11/2,1/2)

Answer 7

x = 3y+4. then substitute 3y+4 into the other equation as x. therefore, -3(3y+4)+5y=-14.

Answer 8

x-3y=4 , multiply it with 3 = 3x-9y= -12 .............1
-3x +5y= -14......... ....2
Add 1&2 -4y= -26
y= 26/4= 13/2
Sub Value y in 1, x -3*13/2=4, x= 4 +39/2
x= 47/2, y= 13/2.

Answer 9

x=4+3y
-12-9y+5y=-14
-4y = -2 ,,,,y = 1/2 , x=4+3/2,,,x= 8+3 /2 = 11/2

Answer 10

x = 4 + 3y
- 12 - 9y + 5y = - 14
- 4y = - 2
y = 1/2

x - 3/2 = 4
x = 11/2

x = 11/2 , y = 1/2