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Solve the following systems of equations for the unknown variables. Enter your answer in (x,y) format.
y = 2x
x = 9y-2

Sagot :

chibabykalu16

Answer:

(2/17, 4/17)

Step-by-step explanation:

y = 2x ---(1)

x = 9y-2 ---(2)

We have a simultaneous equation, to solve it we can use the substitution method:

What is substitution?

One might ask what's substitution, well simply put it's a way of substituting values from one equation to another.

E.g x = 1 then y = 2x when solving since we know x = 1 the value for y would be 2 * 1 = 2

Solving

Substituting eqn(1) into eqn(2)

Note: eqn means equation (we're all clear now)

x = 9(2x) - 2

x = 18x - 2

18x - x = 2

17x = 2

x = 2/17

Nextly, finding the value of y since we know the value of x we can substitute that into eqn(1)

→ y = 2(2/17)

y = 4/17

Therefore, the answer in the format (x,y)

  • (2/17, 4/17)

The solution is (x, y) = (2/17, 4/17).

Express one variable in terms of the other:

Since we already have x solved for in the second equation:

x = 9y - 2

  • Substitute this expression for x in the first equation:

y = 2(9y - 2)  (Substitute x with 9y-2)

  • Solve for y:

Expand the bracket:

y = 18y - 4

  • Combine like terms:

17y - 4 = 0

  • Add 4 to both sides:

17y = 4

  • Divide both sides by 17:

y = 4/17

  • Solve for x using the value of y:

Now that we know y = 4/17, substitute this value back into the equation where x is already solved for:

x = 9(4/17) - 2

  • Simplify:

x = 36/17 - 2

  • Find a common denominator:

x = 36/17 - 34/17

  • Combine like terms:

x = 2/17.

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