MATH SOLVE

5 months ago

Q:
# Solve system by eliminationy=x^2y=x+2SHOW YOUR WORK

Accepted Solution

A:

we have that

y=x²----> equation 1

y=x+2-----> equation 2

multiply equation 1 by -1

-y=-x²

add equation 1 and equation 2

-y=-x²

y=x+2

------------

0=-x²+x+2-------------> -x²+x+2=0-----> x²-x-2=0

Group terms that contain the same variable, and move the constant to the opposite side of the equation(x²-x)=2

Complete the square. Remember to balance the equation by adding the same constants to each side

(x²-x+0.5²)=2+0.5²

Rewrite as perfect squares(x-0.5)²=2+0.5²

(x-0.5)²=2.25-----> (x-0.5)=(+/-)√2.25-----> (x-0.5)=(+/-)1.5

x1=1.5+0.5-----> x1=2

x2=-1.5+0.5---- > x2=-1

for x=2

y=x²----> y=2²----> y=4

the point is (2,4)

for x=-1

y=x²----> y=(-1)²---> y=1

the point is (-1,1)

the answer is

the solution of the system are the points

(2,4) and (-1,1)

y=x²----> equation 1

y=x+2-----> equation 2

multiply equation 1 by -1

-y=-x²

add equation 1 and equation 2

-y=-x²

y=x+2

------------

0=-x²+x+2-------------> -x²+x+2=0-----> x²-x-2=0

Group terms that contain the same variable, and move the constant to the opposite side of the equation(x²-x)=2

Complete the square. Remember to balance the equation by adding the same constants to each side

(x²-x+0.5²)=2+0.5²

Rewrite as perfect squares(x-0.5)²=2+0.5²

(x-0.5)²=2.25-----> (x-0.5)=(+/-)√2.25-----> (x-0.5)=(+/-)1.5

x1=1.5+0.5-----> x1=2

x2=-1.5+0.5---- > x2=-1

for x=2

y=x²----> y=2²----> y=4

the point is (2,4)

for x=-1

y=x²----> y=(-1)²---> y=1

the point is (-1,1)

the answer is

the solution of the system are the points

(2,4) and (-1,1)