Step: 1

The system contains the equation of a line and a parabola. The maximum number of points of intersection is two. So, there are at most two solutions.

Step: 2

4x + y = 12

[Equation of line.]

Step: 3

[Solve for y .]

Step: 4

[Equation of parabola.]

Step: 5

[Replace y with 12 - 4x .]

Step: 6

[Simplify.]

Step: 7

(x - 6)(x + 2) = 0

[Factor.]

Step: 8

[Solve for x .]

Step: 9

At x = 6, y = 12 - 4(6) = -12

[Simplify.]

Step: 10

At x = - 2, y = 12 - 4(- 2) = 20

[Simplify.]

Step: 11

The points of intersection are (6, -12) and (- 2, 20).

Correct Answer is : (6, -12) and (- 2, 20)

Step: 1

The system contains the equation of a line and a circle. The maximum number of points of intersection is 2. Therefore, there are at most 2 solutions.

Step: 2

[Equation of line.]

Step: 3

[Equation of circle.]

Step: 4

[Replace y with x .]

Step: 5

2x ^{2} = 128

[Simplify.]

Step: 6

[Solve for x .]

Step: 7

At x = 8, y = 8

[Use the equation y = x .]

Step: 8

At x = - 8, y = - 8

[Use the equation y = x .]

Step: 9

The points of intersection (or) the solutions are (8, 8), (- 8, - 8).

Correct Answer is : (8, 8), (- 8, - 8)

Step: 1

Step: 2

Step: 3

[Substitute the value of y of equation 1 in equation 2.]

Step: 4

[Simplify.]

Step: 5

(x - 39)(x - 40) = 0

[Factor.]

Step: 6

Step: 7

At x = 39, y = 39 + 1 = 40

[Use equation 1.]

Step: 8

At x =40, y = 40 + 1 = 41

[Use equation 1.]

Step: 9

So, the solutions of the quadratic linear system are (39, 40) and (40, 41).

Correct Answer is : (39, 40) and (40, 41)

Step: 1

Step: 2

Step: 3

4x - 6 = x ^{2} - 9x + 30

[Substitute the the value of y of equation 1 in equation 2.]

Step: 4

[Simplify.]

Step: 5

(x - 9)(x - 4) = 0

[Factor.]

Step: 6

Step: 7

At x = 9, y = 4(9) - 6 = 30

[Use equation 1.]

Step: 8

At x = 4, y = 4(4) - 6 = 10

[Use equation 1.]

Step: 9

So, the solutions of the quadratic linear system are (9, 30) and (4, 10).

Correct Answer is : (9, 30) and (4, 10)

Step: 1

Step: 2

Step: 3

[Substitute the value of y of equation 1 in equation 2.]

Step: 4

[Simplify.]

Step: 5

(x - 14)(x - 15) = 0

[Factor.]

Step: 6

Step: 7

At x = 14, y = 14 + 1 = 15

[Use equation 1.]

Step: 8

At x = 15, y = 15 + 1 = 16

[Use equation 1.]

Step: 9

So, the solutions of the quadratic linear system are (14, 15) and (15, 16).

Correct Answer is : (14, 15) and (15, 16)

Step: 1

The system contains the equation of a line and a circle. The maximum number of points of intersection is 2. Therefore, there are at most 2 solutions.

Step: 2

[Equation of line.]

Step: 3

[Equation of circle.]

Step: 4

[Replace y with x .]

Step: 5

2x ^{2} = 50

[Simplify.]

Step: 6

[Solve for x .]

Step: 7

At x = 5, y = 5

[Use the equation y = x .]

Step: 8

At x = - 5, y = - 5

[Use the equation y = x .]

Step: 9

The points of intersection (or) the solutions are (5, 5), (- 5, - 5).

Correct Answer is : (5, 5), (- 5, - 5)

Step: 1

The system contains the equation of a line and an ellipse. The maximum number of points of intersection is two, and therefore atmost number of solutions are two.

Step: 2

[Equation of line.]

Step: 3

[Equation of ellipse.]

Step: 4

[Replace y with x .]

Step: 5

[Simplify.]

Step: 6

[Solve for x .]

Step: 7

At x = 2, y = 2

[Use the equation y = x .]

Step: 8

At x = - 2, y = - 2

[Use the equation y = x .]

Step: 9

The points of intersection or solutions are (2, 2), (- 2, - 2).

Correct Answer is : (2, 2), (- 2, - 2)

Step: 1

Step: 2

7x + 4x ^{2} = -3

[Substitute y = 4x ^{2} in 7x + y = -3.]

Step: 3

4x ^{2} + 7x + 3 = 0

Step: 4

(4x + 3)(x + 1)= 0

[Factor.]

Step: 5

x = -3 4 , -1

[Solve for x .]

Step: 6

[substitute x values in y = 4x ^{2}.]

Step: 7

The system of equations has two solutions (- 3 4 , 9 4 ) and (-1, 4).

Correct Answer is : (- 3 4 , 9 4 ) and (-1, 4)

Step: 1

Step: 2

[Substitute y = x ^{2} +3x in x + y = 5.]

Step: 3

Step: 4

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

[Factor.]

Step: 5

[Solve for x .]

Step: 6

At x = -5, (-5) + y = 5

[ Use equation 2.]

Step: 7

Step: 8

At x = 1, (1) + y = 5

[ Use equation 2.]

Step: 9

Step: 10

The system of equations has two solutions (-5, 10) and (1, 4).

Correct Answer is : (-5, 10) and (1, 4)

Step: 1

Step: 2

Step: 3

[Graph the equations 1 and 2.]

Step: 4

From the graph, the solutions of the quadratic linear system are (2, -1) and (3, 1)

Correct Answer is : (2, -1) and (3, 1)

Step: 1

Step: 2

Step: 3

[Equate the values of y , from both the equations.]

Step: 4

x^{2} + 2x - 3 = 0

[Simplify.]

Step: 5

(x - 1)(x + 3) = 0

[Factor.]

Step: 6

[Solve for x .]

Step: 7

At x = 1, y = - (1) +1 = 0

[ Use equation 2.]

Step: 8

At x = - 3, y = - (- 3) + 1 = 4

[ Use equation 2.]

Step: 9

So, the solutions of the quadratic linear system are (1, 0) and (-3, 4).

Correct Answer is : (1, 0) and (-3, 4)

Step: 1

Step: 2

Step: 3

[Graph the equations 1 and 2.]

Step: 4

From the graph, the solutions of the quadratic linear system are (4, 3.3) and (1, -1.2).

Correct Answer is : (1, -1.2) and (4, 3.3)

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