How do you solve the following system?: #4x + 5y = 2 , y + 5 = 3x #

Question

How do you solve the following system?: #4x + 5y = 2   ,   y + 5 = 3x  #

Abigail Allen · Accepted Answer

#x = 27/19# and #y = -14/19#

Let's isolate #y# in the second equation

#y = 3x - 5#

Now we can solve for #x# in the other equation

#4x + 5 (3x - 5) = 2#

#4x + 15x -25 = 2#

#19x = 27#

#x = 27/19#

Now we solve for #y#

#y = 3x - 5#

#y = 3 (27/19) - 5#

#y = 81/19 - 5/1 xx 19/19#

#y = 81/19 - 95/19#

#y = -14/19#

To check our work, let's substitute #27/19# for #x# and #-14/19# for #y# in the first equation and solve.

#4(27/19) + 5(-14/19) = 2#

#108/19 - 70/19 = 38/19#

#38/19 = 2 = 2#!

We were accurate!

Eva Adamson · Answer

#color(blue)(x = 27/19), color(purple)(y = -14 / 19)#

#4x + 5y = 2# Eqn (1)

#y + 5 = 3x#

#y = 3x - 5# Eqn (2)

Changing the value of the y term in Eqn (1) to x,

#4x + 5(3x - 5) = 2#

#4x + 15x - 25 = 2#

Constants on R H S, variables on L H S rearranged,

#4x + 15x = 27#

#19x = 27# or #x = 27/19#

Changing the value of x in Equation (2),

# y = 3x - 5 = (3 * (27 / 19)) - 5 = (81 - 95) / 19 = -14/19#

Eva Abramson · Answer

undefined To solve the system of equations:

4x + 5y = 2
y + 5 = 3x

1. Rearrange the second equation to solve for y:
   y = 3x - 5

2. Substitute the expression for y from the second equation into the first equation:
   4x + 5(3x - 5) = 2

3. Simplify and solve for x:
   4x + 15x - 25 = 2
   19x - 25 = 2
   19x = 27
   x = 27/19

4. Substitute the value of x into either of the original equations to solve for y. Using the second equation:
   y = 3(27/19) - 5
     = 81/19 - 5
     = 81/19 - 95/19
     = -14/19

So, the solution to the system is x = 27/19 and y = -14/19.