Solve the system of equations. {:[y=-4x],[y=2x^(2)-15 x]:} solutions = ( ◻ and ◻ )

Set Equation to Zero: Now, we will move all terms to one side to set the equation to zero and solve for x. 0 = 2x^2 - 15x + 4x 0 = 2x^2 - 11xFactor Quadratic Equation: Next, we factor the quadratic equation to find the values of x. 0 = x(2x - 11) This gives us two solutions: x = 0 and 2x - 11 = 0.Solve for x: Solving the second equation 2x - 11 = 0 for x gives us: 2x = 11 x = 11/2 x = 5.5Substitute Values for y: Now we have two values for x: x = 0 and x = 5.5. We will substitute these values back into one of the original equations to find the corresponding y values. First, for x = 0: y = -4(0) y = 0Final Solutions: Next, for x = 5.5: y = -4(5.5) y = -22We now have two solutions for the system of equations: (0, 0) and (5.5, -22).

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Find indefinite integrals using the substitution

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Q. Solve the system of equations.

\newline

\begin{array}{l} y=-4 x \\ y=2 x^{2}-15 x \end{array}

\newline

solutions

= (

\square

and

\square )

Set Equation to Zero: Now, we will move all terms to one side to set the equation to zero and solve for $x$ . $0 = 2x^2 - 15x + 4x$ $0 = 2x^2 - 11x$
Factor Quadratic Equation: Next, we factor the quadratic equation to find the values of $x$ . $0 = x(2x - 11)$ This gives us two solutions: $x = 0$ and $2x - 11 = 0$ .
Solve for x: Solving the second equation $2x - 11 = 0$ for x gives us: $\newline$ $2x = 11$ $\newline$ $x = \frac{11}{2}$ $\newline$ $x = 5.5$
Substitute Values for y: Now we have two values for x: $x = 0$ and $x = 5.5$ . We will substitute these values back into one of the original equations to find the corresponding y values. $\newline$ First, for $x = 0$ : $\newline$ $y = -4(0)$ $\newline$ $y = 0$
Final Solutions: Next, for $x = 5.5$ : $y = -4(5.5)$ $y = -22$
Final Solutions: Next, for $x = 5.5$ : $y = -4(5.5)$ $y = -22$ We now have two solutions for the system of equations: $(0, 0)$ and $(5.5, -22)$ .