Question

Solve the system of equations:

y=x-2
y=x²-3x+2

A. (0, -2)
B. (1, -1) and (3,1)
C. (2,0)
D. (2,0) and (1,0)

Answer 1

Answer:

  C.  (2, 0)

Step-by-step explanation:

The solution to this system of equations is the set of (x, y) values that satisfy both equations. It is the set of points where their graphs intersect.

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graph

A graph (attached) shows the only solution to be the point (2, 0), where the line is tangent to the parabola.

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algebraic

We can equate the two expressions for y to arrive at an algebraic solution.

  x -2 = x² -3x +2

  x -2 = (x -2)(x -1) . . . . factor the right side

  0 = (x -2)(x -1 -1) . . . . subtract (x-2) from both sides

  0 = (x -2)² . . . . simplify

  x = 2 . . . . . . the only value of x that satisfies this equation

  y = x -2 = 2 -2 = 0 . . . . the corresponding value of y

The one solution is (x, y) = (2, 0).

Answer 2

Given the system of equations: y=x-2 and y=x²-3x+2. The one solution is (x, y) = C.  (2, 0). Option C is correct.

What is a system of equations?

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given the system of equations:

y=x-2

y=x²-3x+2

A graph shows the only solution to be the point (2, 0), where the line is tangent to the parabola.

We can equate the two expressions for y;

x -2 = x² -3x +2

x -2 = (x -2)(x -1)

0 = (x -2)(x -1 -1)

0 = (x -2)²

simplify

x = 2

 y = x -2 = 2 -2 = 0

Hence, The one solution is (x, y) = (2, 0). Option C is correct.

Learn more about equations here;

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