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Solve 2y+x=8 ,1+y=2x

2 Answers

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Answer:

To solve the system of equations 2y+x=8 and 1+y=2x, we can use the method of substitution or elimination.

Method 1: Substitution

Step 1: Solve one of the equations for one variable in terms of the other variable. Let's solve the second equation for y:

1 + y = 2x

Subtract 1 from both sides:

y = 2x - 1

Step 2: Substitute the expression for y from step 1 into the other equation:

2y + x = 8

Replace y with 2x - 1:

2(2x - 1) + x = 8

Simplify:

4x - 2 + x = 8

Combine like terms:

5x - 2 = 8

Step 3: Solve the resulting equation for x:

5x - 2 = 8

Add 2 to both sides:

5x = 10

Divide both sides by 5:

x = 2

Step 4: Substitute the value of x back into one of the original equations to find y. Let's use the first equation:

2y + x = 8

Replace x with 2:

2y + 2 = 8

Subtract 2 from both sides:

2y = 6

Divide both sides by 2:

y = 3

Therefore, the solution to the system of equations is x = 2 and y = 3.

Method 2: Elimination

Step 1: Multiply one or both of the equations by a constant to make the coefficients of one variable equal in both equations. Let's multiply the second equation by 2 to eliminate the y terms:

2(1 + y) = 2(2x)

2 + 2y = 4x

Step 2: Subtract the resulting equation from the first equation to eliminate the y terms:

(2y + x) - (2 + 2y) = 8 - 4x

2y + x - 2 - 2y = 8 - 4x

Simplify:

x - 2 = 8 - 4x

Step 3: Solve the resulting equation for x:

x - 2 = 8 - 4x

Add 4x to both sides:

5x - 2 = 8

Add 2 to both sides:

5x = 10

Divide both sides by 5:

x = 2

Step 4: Substitute the value of x back into one of the original equations to find y. Let's use the first equation:

2y + x = 8

Replace x with 2:

2y + 2 = 8

Subtract 2 from both sides:

2y = 6

Divide both sides by 2:

y = 3

Therefore, the solution to the system of equations is x = 2 and y = 3

Explanation:

<3

User Teddybeard
by
7.6k points
1 vote

Answer:

y = 3

y = 3x = 2

Explanation:

2y + x = 8

x = 8 - 2y

x = 2(4 - y)

Substitute in the other equation.

1 + y = 2x

1 + y = 2 ( 2(4-y))

1 + y = 2 (8 - 2y)

1 + y = 16 - 4y

1 - 16 = - 4y - y

- 15 = - 5y

15 = 5y

15/5 = y

3 = y

x = 8 - 2y

x = 8 - 2(3)

x = 8 - 6

x = 2

__________

hope this helps!

User Sergej Werfel
by
8.4k points

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