We want to solve the following system of equations. {[y=4x(x-2)],[x+y=2]:} One of the solutions to this system is (2,0). Find the other solution. Your answer must be exact.

Question

We want to solve the following system of equations.  {[y=4x(x-2)],[x+y=2]:} One of the solutions to this system is  (2,0). Find the other solution. Your answer must be exact.

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Substitute and simplify: Substitute the expression for y from the first equation into the second equation. We have y = 4x(x - 2) and x + y = 2. Substituting y in the second equation gives us x + 4x(x - 2) = 2.Expand and combine like terms: Expand the equation x + 4x(x - 2) = 2. This gives us x + 4x^2 - 8x = 2.Factor the quadratic equation: Simplify the equation by combining like terms. This results in 4x^2 - 7x + 2 = 0.Solve for x: Factor the quadratic equation 4x^2 - 7x + 2 = 0. The factors of this quadratic equation are (4x - 1)(x - 2) = 0.Substitute and simplify: Solve for x by setting each factor equal to zero. Setting 4x - 1 = 0 gives us x = 1/4. Setting x - 2 = 0 gives us x = 2, but we already know that (2,0) is one solution, so we are looking for the other solution.Check the solution: Substitute x = 1/4 into the first equation to find the corresponding value of y. Substituting into y = 4x(x - 2) gives us y = 4*(1/4)*((1/4) - 2).Simplify the expression to find the value of y. This gives us y = 4*(1/4)*(-7/4), which simplifies to y = -7.Check the solution (1/4, -7) in the second equation x + y = 2. Substituting x = 1/4 and y = -7 into the equation gives us 1/4 - 7 = 2, which simplifies to -27/4 ≠ 2. There is a math error in the previous steps.

We want to solve the following system of equations. $\newline$ $\left\{\begin{array}{l} y=4 x(x-2) \\ x+y=2 \end{array}\right.$ $\newline$ One of the solutions to this system is $(2,0)$ . $\newline$ Find the other solution. $\newline$ Your answer must be exact.

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We want to solve the following system of equations.\newline{y=4x(x−2)x+y=2 \left\{\begin{array}{l} y=4 x(x-2) \\ x+y=2 \end{array}\right. {y=4x(x−2)x+y=2​\newlineOne of the solutions to this system is (2,0) (2,0) (2,0).\newlineFind the other solution.\newlineYour answer must be exact.

We want to solve the following system of equations. $\newline$ $\left\{\begin{array}{l} y=4 x(x-2) \\ x+y=2 \end{array}\right.$ $\newline$ One of the solutions to this system is $(2,0)$ . $\newline$ Find the other solution. $\newline$ Your answer must be exact.