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What values of x and y satisfy the system of equations {3x+2y=14 x=4y−2?

User Abilash A
by
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1 Answer

3 votes

Answer:

x = 26/7

y = 10/7

Explanation:

To find the values of x and y that satisfy the system of equations:

1. 3x + 2y = 14

2. x = 4y - 2

You can solve this system using the substitution method. Start by solving equation (2) for x:

x = 4y - 2

Now, substitute this expression for x into equation (1):

3(4y - 2) + 2y = 14

Now, distribute the 3 on the left side:

12y - 6 + 2y = 14

Combine like terms:

14y - 6 = 14

Add 6 to both sides of the equation:

14y = 14 + 6

14y = 20

Now, divide by 14 to solve for y:

y = 20 / 14

y = 10 / 7

Now that you have found the value of y, you can substitute it back into equation (2) to find x:

x = 4(10 / 7) - 2

x = (40 / 7) - (14 / 7)

x = (40 - 14) / 7

x = 26 / 7

So, the values that satisfy the system of equations are:

x = 26/7

y = 10/7

User Mikestreety
by
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