How do you solve this by elimination method? 4x+3y=016x+3=8y
4 x + 3 y = 0
16 x + 3 = 8y
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Multiply the first equation by 4
16 x + 12 y = 0
16 x + 3 = 8y
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Subtract 8 y by second equation
16 x + 12 y = 0
16 x + 3 - 8 y = 8y - 8y = 0
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16 x + 12 y = 0
16 x + 3 - 8 y = 0
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Subtract 3 by second equation
16 x + 12 y = 0
16 x + 3 - 8 y - 3 = 0 - 3
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16 x + 12 y = 0
16 x - 8 y = - 3
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Subtract fsecond equation from first equation
16 x - 1 6 x + 12 y - ( - 8 y ) = 0 - ( - 3 )
12 y + 8 y = 3
20 y = 3 Divide both sides by 20
y = 3 / 20
Put y = 3 / 20 in first equation.
4 x + 3 y = 0
4 x + 3 * 3 / 20 = 0
4 x + 9 / 20 = 0 Subtract 9 / 20 by both sides
4 x + 9 / 20 - 9 / 20 = 0 - 9 / 20
4 x = - 9 / 20 Divide both sides by 4
x = - 9 / ( 20 * 4 )
x = - 9 / 80
Solution :
x = - 9 / 80 , y = 3 / 20
To solve the system of equations by the elimination method, follow these steps:
1. Write the given system of equations:
4x + 3y = 0
16x + 3 = 8y
2. Multiply the second equation by 4 to eliminate the y term:
16x + 12 = 32y
3. Now, we have two equations:
4x + 3y = 0
16x + 12 = 32y
4. Next, we need to choose which variable to eliminate. In this case, it is convenient to eliminate the y term.
5. To do that, we can multiply the first equation by 8 and the second equation by 3 to make the coefficients of y equal:
(8)(4x + 3y) = (8)(0)
(3)(16x + 12) = (3)(32y)
Simplifying these equations gives us:
32x + 24y = 0
48x + 36 = 96y
6. Now, subtract the equation obtained in step 5 from the equation obtained in step 3. This eliminates the y term:
(48x + 36 = 96y) - (32x + 24y = 0)
Simplifying further, we get:
16x + 12 = 72y
7. Rearrange the equation:
16x = 72y - 12
8. Simplify the equation:
16x = 72y - 12
9. Divide by 8:
x = (72y - 12)/16
10. Simplify the equation further:
x = (9y - 3)/2
11. Substitute this value of x back into one of the original equations (either equation 1 or 2) to solve for y.
Once you have found the value of y, you can substitute it into either equation to find the value of x.