Write as a Vector Equality y=x^2-5x+1 , x+y=-2

Problem

y=x2−5*x+1,x+y=−2

Solution

1. Rearrange the second equation to solve for y in terms of x

y=−x−2

2. Set the two expressions for y equal to each other to find the intersection points.

x2−5*x+1=−x−2

3. Move all terms to one side to form a quadratic equation.

x2−4*x+3=0

4. Factor the quadratic equation.

(x−1)*(x−3)=0

5. Solve for x by setting each factor to zero.

x=1,x=3

6. Substitute the x values back into the linear equation y=−x−2 to find the corresponding y values.

(y_1)=−(1)−2=−3

(y_2)=−(3)−2=−5

7. Express the solution as a vector equality by grouping the x and y coordinates into vectors.

([x],[y])=([1],[−3]),([3],[−5])

Final Answer

([x],[y])=([1],[−3]),([3],[−5])

Want more problems? Check here!