Solve the system of equations.y=x2−50x−50y=−50x+31Write the coordinates in exact form. Simplify all fractions and radicals.(______,______)(______,______)
Q. Solve the system of equations.y=x2−50x−50y=−50x+31Write the coordinates in exact form. Simplify all fractions and radicals.(______,______)(______,______)
Set Equations Equal: We have the following system of equations:y=x2−50x−50y=−50x+31To find the solution, we will set the two equations equal to each other since they both equal y.x2−50x−50=−50x+31
Simplify Quadratic Equation: Simplify the equation by moving all terms to one side to form a quadratic equation.x2−50x−50+50x−31=−50x+31+50x−31x2−81=0
Solve for x: Solve the quadratic equation for x.x2=81Take the square root of both sides.x=±81x=±9
Find y-values: Find the corresponding y-values for each x-value by substituting back into one of the original equations. We can use y=−50x+31. For x=9: y=−50(9)+31y=−450+31y=−419
Find Second y-value: Find the y-value for the second x-value.For x=−9:y=−50(−9)+31y=450+31y=481
Write Coordinates: Write the coordinates in exact form.The solutions to the system of equations are the points where the two graphs intersect.First Coordinate: (9,−419)Second Coordinate: (−9,481)
More problems from Solve a system of linear and quadratic equations: parabolas