SOLUTION: find the intersection of these two lines... 3x=2+4y 2y=6-5x I can not figure this out to save my life!!

Question 216281: find the intersection of these two lines...
3x=2+4y
2y=6-5x
I can not figure this out to save my life!!
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
find the intersection of these two lines...

Equation A
Equation B

Step 1. Let's put the variable terms x and y on the left side and numbers on the right side of equation as given by Step 2.

Step 2. For Equation A, subtract 4y to both sides of the equation and; for equation B add 5x to both sides of the equation.

Equation A-1
Equation B-1

Step 3. Multiply 2 to both sides of Equation B-1 to get

Equation A-1
Equation B-2

Step 4. Add Equations A-1 and B-2 and note the y-terms cancel each other out leaving the x-terms on the left side.

or

Step 5. Substitute this value of x into either Equations A-1 or B-2. Let's choose Equation A-1.
Equation A-1

Multiply by 13 to both sides of equation to get rid of denominator

Add 52y-26 to both sides of equation

Divide 52 to both sides of the equation

Step 6. ANSWER: So x=14/13 and y=4/13 or the intersection point is (14/13,4/13).

We can verify the above result by substituting these values into both equations to see if it leads to a true statement.

Here's another approach to solving the linear system equations by substitution:

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION

Solve:
We'll use substitution. After moving -4*y to the right, we get:
, or . Substitute that
into another equation:
and simplify: So, we know that y=0.307692307692308. Since , x=1.07692307692308.

Answer: .

Same result as before.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit
http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit
http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

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