SOLUTION: I need help to show me how to work out the use the substitution to solve the equations and state if it has no solution or infinitely many solutions: 2x+7y=3 x=1-4y

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Question 386322: I need help to show me how to work out the use the substitution to solve the equations and state if it has no solution or infinitely many solutions: 2x+7y=3 x=1-4y
Found 2 solutions by stanbon, Earlsdon:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
I need help to show me how to work out the use the substitution to solve the equations and state if it has no solution or infinitely many solutions: 2x+7y=3 x=1-4y
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Substitute for "x" and solve for "y":
2(1-4y) + 7y = 3
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2 - 8y + 7y = 3
2 -y = 3
y = 2-3
y = -1
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Since x = 1-4y, solve for "x":
x = 1-4*(-1)
x = 5
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Check the answer:
2x+7y=3
2(5)+7(-1) = 3
10-7 = 3
3 = 3
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Solution: (5,-1)
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Cheers,
Stan H.

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve by substitution:
2x%2B7y+=+3
x+=+1-4y Substitute this x into the first equation then solve for y.
2%281-4y%29%2B7y+=+3 Simplify.
2-8y%2B7y+=+3
2-y+=+3 Subtract 2 from both sides.
-y+=+1 Multiply by -1 to make y positive.
y+=+-1 Now substitute this value of y into either one of the two given equations and solve for x. Let's use the second equation.
x+=+1-4y Substitute y+=+-1
x+=+1-4%28-1%29 Simplify.
x+=+1%2B4
x+=+5
The solution is: (5, -1)
Let's look at the graphic solution:
graph%28400%2C400%2C-2%2C10%2C-2%2C1%2C-%282%2F7%29x%2B3%2F7%2C-%281%2F4%29x%2B1%2F4%29
The solution is where the two lines intersect (5, -1)