SOLUTION: Please help me solve using the elimination method. If the system has an infinite # of solutions, use set-builder notation to write the solution set. If the system has no solution,s

Algebra ->  Graphs -> SOLUTION: Please help me solve using the elimination method. If the system has an infinite # of solutions, use set-builder notation to write the solution set. If the system has no solution,s      Log On


   

Question 225884: Please help me solve using the elimination method. If the system has an infinite # of solutions, use set-builder notation to write the solution set. If the system has no solution,state this.

x-6y=7
2x-6y=2
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Solve by elimination

x-6y=7 Equation A
2x-6y=2 Equation B

Step 1. Subtract Equation B from Equation A to eliminate the y-term

%28x-6y%29-%282x-6y%29=7-2

x-6y-2x%2B6y=5

-x=5

Step 2. Multiply by -1 to both sides to get x=-5

Step 3. Substitute x=-5 into Equation A x-6y=7+ to find y

-5-6y=7+

Add 5 to both sides of the equation to get numbers on one side and variable y on the other side.

-5-6y%2B5=7%2B5+

-6y=7%2B5+

-6y=12

Divide by -6 to both sides of the equation

-6y%2F-6=12%2F-6

y=-2

Step 4. Check x=-5 and y=-2 is solution to Equation B 2x-6y=2

2%2A%28-5%29-6%2A%28-2%29=2

-10%2B12=2

2=2 which is a true statement.

Step 5. ANSWER: The solution is x=-5 and y=-2 or (-5,-2) which is the intersection between these two lines or system of linear equations.

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J