How do you solve x+5y=4 and 3x+15y=-1 using substitution?

x+5y=4
3x+15y=-1

2 Answers
mimi
Mar 21, 2018

#(-2.5, 1.3)#

Explanation:

SUBSTITUTION means substituting one of the variables for a different value in an equation, which can allow you to solve the equation.

  1. To get the value of one of the variables, isolate the variable in one of the equations (choose the simpler equation to make life easier).
    #x+5y=4#
    #x=4-5y#

  2. Substitute (hence the method name "substitution") #x# in the other equation for the value of #x#.
    #3color(blue)x+5y=-1#
    #3color(blue)((4-5y))+5y=-1#

  3. Now that we have like variables in the equation, we can solve for #y#.
    #3(4-5y)+5y=-1#
    #12-15y+5y=-1#
    #12-10y=-1#
    #-10y=-13#
    #y=13/10=1.3#

  4. Now that we know the value of #y#, substitute it back into the first equation and solve for #x#.
    #x=4-5color(green)y#
    #x=4-5color(green)((1.3))#
    #x=4-6.5#
    #x=-2.5#

Answer (Coordinate Form): #(-2.5, 1.3)#

Blake Gunnels
Mar 21, 2018

y=-0.5
x=6.5

Explanation:

Get x by it's self in the first equation which is #x=-5y+4# then you insert #-5y+4# into where x is in the second equation #3x(-5y+4)+15y=-1# the solve for y, getting you -0.5. Then you do #x+5(-0.50)=4# getting you 6.5.

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