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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
find the intersection of these two lines...

3x=2%2B4y Equation A
2y=6-5x 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.

3x-4y=2%2B4y-4y=2 Equation A-1
5x%2B2y=6-5x%2B5x=6 Equation B-1

Step 3. Multiply 2 to both sides of Equation B-1 to get 10x%2B4y=12


3x-4y=2 Equation A-1
10x%2B4y=12 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.

3x-4y%2B10x%2B4y=2%2B12

13x=14 or x=14%2F13

Step 5. Substitute this value of x into either Equations A-1 or B-2. Let's choose Equation A-1.
3x-4y=2 Equation A-1

3%2A14%2F13-4y=2

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

42-4%2A13y=2%2A13

42-52y=26

Add 52y-26 to both sides of equation

42-52y%2B52y-26=26%2B52y-26

16=52y

Divide 52 to both sides of the equation

16%2F52=52y%2F52

y=4%2F13

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:
+system%28+%0D%0A++++3%5Cx+%2B+-4%5Cy+=+2%2C%0D%0A++++5%5Cx+%2B+2%5Cy+=+6+%29%0D%0A++We'll use substitution. After moving -4*y to the right, we get:
3%2Ax+=+2+-+-4%2Ay, or x+=+2%2F3+-+-4%2Ay%2F3. Substitute that
into another equation:
5%2A%282%2F3+-+-4%2Ay%2F3%29+%2B+2%5Cy+=+6 and simplify: So, we know that y=0.307692307692308. Since x+=+2%2F3+-+-4%2Ay%2F3, x=1.07692307692308.

Answer: system%28+x=1.07692307692308%2C+y=0.307692307692308+%29.



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