SOLUTION: 2x+2y=16 2x+6y=28

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Question 189479: 2x+2y=16
2x+6y=28

Found 2 solutions by jojo14344, greta_elisif:
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


Givensystem%282x%2B2y=16%28red%28EQN1%29%29%2C2x%2B6y=28%28red%28EQN2%29%29%29

In red%28EQN1%29 we get,
2y=-2x%2B16--->cross%282%29y%2Fcross%282%29=%28-2x%2B16%29%2F2=%28-2%2F2%29x%2B16%2F2
y=-x%2B8red%28EQN3%29, subst. in red%28EQN2%29:

2x%2B6%28red%28-x%2B8%29%29=28
2x-6x%2B48=28----> -4x=28-48=-20--->cross%28-4%29x%2Fcross%28-4%29=cross%28-20%295%2Fcross%28-4%29
red%28x=5%29, subst. in red%28EQN3%29:

y=-red%285%29%2B8=red%283%29

Then, these two lines intersect at point (5,3)

We'll see,
--->RED=EQN1; GREEN=EQN2

Thank you,
Jojo


Answer by greta_elisif(10) About Me  (Show Source):
You can put this solution on YOUR website!
Solve 1 equation for 1 variable:
1. Subtract 2y from both sides to move it out of the way:
2x+%2B+2y+-+2y+=+16+-+2y
2x+=+16+-+2y
2. Divide both sides by 2 to move it out of the way:
2x%2F2+=+%2816+-+2y%29%2F2
3. Regroup fraction on the right side:
2x%2F2+=+16%2F2+-+2y%2F2
4. Cancel 2s and divide 16 by 2:
x+=+8+-+y
..
Solve to get one answer:
5. Replace the variable in the other equation with your answer:
2%288+-+y%29+%2B+6y+=+28
Distribute the 2
16+-+2y+%2B+6y+=+28
16+%2B+4y+=+28
6. Subtract 16 from both sides to move it out of the way:
16+%2B+4y+-+16+=+28+-+16
4y+=+12
7. Divide by 4 to get to y:
4y%2F4+=+12%2F4
y+=+3
..
Put this answer in an equation to get the other answer:
8. Replace y with what it equals:
x+=+8+-+y
x+=+8+-+3
9. Subtract to get the second answer:
x+=+5
..
Check:
10. Use first equation:
2x%2B2y=16
11. Replace variables with what they equal:
2%285%29+%2B+2%283%29+=+16
12. Multiply:
10+%2B+6+=+16
13. Add:
16+=+16
..
Check more:
14. Use second equation:
2x%2B6y=28
15. Replace variables with what they equal:
2%285%29+%2B+6%283%29+=+28
16. Multiply:
10+%2B+18+=+28
17. Add:
28+=+28