Question

solve the system of equations

1: y=3x^2-2x-1

2x+3y=2

2: x^2+(y-2)^2=4

x^2-2y=0

Answer #1

y = 3x^{2} -2x-1

(2-2x)/3 = 3x^{2} - 2x - 1

2-2x = 9x^{2} - 6x - 3

9x^{2} -4x -5=0;

9x^{2} - 9x + 5x - 5 =0

9x (x-1) + 5 (x-1) =0

(9x+5) ( x-1) = 0

x=1 or x= -5/9;

if x=1 then y= 2-2 / 3 = 0

if x=-5/9, y = (2- (-10/9) ) /3 = 28/27

Thus, (x,y) = (1,0) or (-5/9, 28/27)

2) x^{2} -2y =0 so x^{2} = 2y

x^{2} + (y-2)^{2} = 4

substituting x^{2} = 2y we get

2y + (y-2)^{2} = 4

2y+ y^{2} -4y + 4 = 4

y^{2} - 2y=0;

y(y-2) =0

y=0 or y=2

if y=0 then x= sqrt(4-4) = 0

if y=2 then x^{2} = 4 ; So x= sqrt(4) = 2

Thus, (x,y) = (0,0) or (2 , 2)

Solve each system of equations
x-2y+3z=7
2x+y+z=4
-3x+2y-2z=-10

Solve the IVP using the Eigenvalue method.
x'=2x-3y+1
y'=x-2y+1
x(0)=0
y(0)=1
x'=2x-3y+1
y'=x-2y+1
x(0)=0
y(0)=1
Solve
the IVP using the Eigenvalue method.
x'=2x-3y+1
y'=x-2y+1
x(0)=0
y(0)=1

1) Solve these equations: 3x-y=-11
x+2y=8
2) Solve these equations:
x+y+z=6
x-y-z=-4
2x+y-4z=-8

1.Solve the system of equations. 2x + 3y = 6 and x – y = ½
2.Is x = y2 a function?
3.Which do we use to determine if a graph represents a
function?
4.Find the average rate of change from 2 to 5 for the function,
f(x) = -4x + 1.
5.What are the slope and y-intercept for the function, h(x) =
-3x + 4?

Solve the system of equations using an inverse matrix
-4x-2y+z= 6
-x-y-2z= -3
2x+3y-z= -4
Choose one:
a. (-1, 0, -2)
b. (1, 0, -2)
c. (1, 0, 2)
d. (-1, 0, 2)

Solve the following system of equations. 2x-3y+z=2 13x-7z=-5
3x+y=2

Solve the following system of equations.
{−x+4y−z=-4
3x−y+2z=6
2x−3y+3z=−2
Give your answer as an ordered triple
(x,y,z).

Solve this system of equations
−2x−3y=−17
−3x+2y=−6
One solution:
No solution
Infinite number of solutions

1. solve the system of equations:
x+3y=9
3x+9y=27
please solve to get the x and y solution
2. solve the system of equations, please state the x and y
solution
9x-4y=23
15x+4y=41
3. solve the system of equations please state the x and y
solution
x - y - z = 1
5x + 6y + z = 1
30x + 25y = 0

1. Solve the following system of equations by the elimination
method:
2x+y-z=7
x+2y+z=8
x-2y+3z=2
2. Solve the following system of equations by using row
operations on a matrix:
2x+y-z=7
x+2y+z=8
x-2y+3z=2

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