SOLUTION: How do I solve the system using the substitution method and show work? 2x+3y=2 x+3y=10

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: How do I solve the system using the substitution method and show work? 2x+3y=2 x+3y=10      Log On


   

Question 280013: How do I solve the system using the substitution method and show work?
2x+3y=2
x+3y=10
Found 2 solutions by nabla, jsmallt9:
Answer by nabla(475) About Me  (Show Source):
You can put this solution on YOUR website!
Subtract the second equation from the first. You get
x=-8
Put that into the second (or first) equation to get y:
y=6
-----------
If you have difficulty understanding this material it is precisely due to pedantic requirements and a lack of intuitive explanations.

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
(A solution provided by another tutor did not use the Substitution Method.)

Substitution Method
  1. Solve one equation (either one) for one of the variables (either one). (Make it easy on yourself and choose the equation and the variable that make this easiest.)
  2. In the equation not used in step #1, substitute for the "solved for" variable of step #1. This results in an equation of just the "solved for" variable.
  3. Solve the one variable equation from Step #2.
  4. Use this value from step #3 and one of the original equations to find the value for the other variable.

Let's see how this works on your system of equations:
2x + 3y = 2
x + 3y = 10
1. Solve one equation for one of the variables. Look for a variable with a coefficient of 1 (or -1), if any. If there is such a variable, this will be a good choice. So I am going to solve the second equation for x. All I have to do is add -3y to (or subtract 3y from) each side. This gives me:
x = -3y + 10

2. Substitute for this variable in the other equation. We used the second equation for step 1 so we will substitute for x in the first equation, using the expression we got in step 1:
2(-3y + 10) + 3y = 2
(Notice the use of parentheses. This is important when making substitutions. In this case it helps us know that the Distributive Property will be needed.) We now have an equation with one variable, y.

3. Solve this one variable equation.
Simplify:
-6y + 20 + 3y = 2
-3y + 20 = 2
Isolate the variable term (by subtracting 20 from each side):
-3y = -18
Divide by -3:
y = 6

4. Use this result to find the other variable by substituting into one of the original equations:
2x + 3(6) = 2
2x + 18 = 2
2x = -16
x = -8

So the solution for this system is (-8, 6).