−3y−4y−4x−2x2amp;=9x+2amp;=3If (x,y) is a solution to the system of equations shown, which of the following are x-coordinates of the solutions?Choose 1 answer:(A) 25 and 1(B) −25 and −1(C) −1 and 1(D) −25 and 211
Q. −3y−4y−4x−2x2=9x+2=3If (x,y) is a solution to the system of equations shown, which of the following are x-coordinates of the solutions?Choose 1 answer:(A) 25 and 1(B) −25 and −1(C) −1 and 1(D) −25 and 211
Write Equations: Write down the system of equations.−3y−4=9x+2y−4x−2x2=3We need to solve this system to find the x-coordinates of the solutions.
Solve for y: Solve the first equation for y.−3y=9x+6y=−(9x+6)/3y=−3x−2Now we have y in terms of x.
Substitute y into 2nd equation: Substitute the expression for y from Step 2 into the second equation.−3x−2−4x−2x2=3Combine like terms.−2x2−7x−2=3
Set equation to zero: Move all terms to one side to set the equation to zero.−2x2−7x−2−3=0−2x2−7x−5=0Now we have a quadratic equation.
Factor or use quadratic formula: Factor the quadratic equation, if possible.The quadratic equation −2x2−7x−5=0 does not factor easily, so we will use the quadratic formula to find the roots.The quadratic formula is x=2a−b±b2−4ac where a, b, and c are the coefficients from the quadratic equation ax2+bx+c=0.For our equation, a=−2, b=−7, and c=−5.
Calculate discriminant: Calculate the discriminant b2−4ac.Discriminant D=(−7)2−4(−2)(−5)D=49−40D=9Since the discriminant is positive, we will have two real solutions.
Use quadratic formula for x: Use the quadratic formula to find the x-coordinates.x=2(−2)−(−7)±9x=−47±3Now we have two solutions for x.
Calculate solutions for x: Calculate the two solutions for x.First solution:x=−47+3x=−410x=−25Second solution:x=−47−3x=−44x=−1The x-coordinates of the solutions are −25 and −1.