How do you solve #x+2y=3# and #3x-y= -5#?

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Answer 1 · 2015-08-05T22:27:00

#color(red)(x=-1, y=2)#

One way is to use the method of substitution.

Step 1. Enter the equations.

[1] #x+2y=3#
[2] #3x-y=-5#

Step 2. Solve for one variable in terms of the other.

Solve Equation 2 for #y#.

[3] #y=3x+5#

Step 3. Substitute Equation 3 in Equation 1 and solve for #x#.

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

#x+6x+10=3#

#7x=-7#

[4] #x=-1#

Step 4. Substitute Equation 4 in Equation 1:

#-1+2y=3#

#2y=4#

#y=2#

The solution is #x=-1, y=2#.

Check:

Substitute the values in Equation 2.

#3x-y=-5#

#3(-1)-2=-5#

#-3-2=-5#

#5=5#

It works!