SOLUTION: y=x-13 2x+3y=1 *Please show me how to do this, I want to learn (relearn) so I can help my daughter. Please show me the steps and not just the answer*

Algebra ->  Expressions-with-variables -> SOLUTION: y=x-13 2x+3y=1 *Please show me how to do this, I want to learn (relearn) so I can help my daughter. Please show me the steps and not just the answer*      Log On


   

Question 1049211: y=x-13
2x+3y=1
*Please show me how to do this, I want to learn (relearn) so I can help my daughter. Please show me the steps and not just the answer*
Answer by advanced_Learner(501) About Me  (Show Source):
You can put this solution on YOUR website!
y=x-13 (1)
2x%2B3y=1 (2)

first Method Substitution

y=x-13 subsitute eq(1) into eq(2)
2x%2B3y=1
2x%2B3%28x-13%29=1 distribute the 3
2x%2B3x-39%29=1
5x-39%29=1 add 39 to both sides
5x%29=1%2B39
5x%29=40 divide both sides by 5
5x%29=40
x%29=8
if x%29=8 then y=x-13 becomes
y=8-13
y=-5
second method elimination
y=x-13 (1) turn this equation into standard form


y-x=-13 (1)
2x%2B3y=1 (2)
now re-arrange
-x+y=-13 (1)
2x%2B3y=1 (2)

multiply eq(1) by 2 on both sides
-2x+2y=-26 (1)
add eq(1) and (2)
-2x+2y=-26
2x%2B3y=1
5y=-25
y=-5
then find the value of x
-x+-5=-13
-x=-13+5
x=8