Question

3) y> 4x -3 y2- 2x +3 ...


Solve the following systems of inequalities graphically then give three ordered pairs satisfying the inequalities. Show that the ordered pairs satisfy the inequalities.

Transcribed: 3) y> 4x -3 y2- 2x +3

Answer

Given that,

y>4x-3y-2x+3

Write the given inequality in equation form,

y=4x-3          ...(1)y=-2x+3      ...(2)

Equation (1),

When x = 0, y=-3,

When y = 0, x=34=0.75

Equation (1) passes through (0, -3) and (0.75, 0).

Equation (2),

When x = 0, y = 3

When y = 0, x=32=1.5

Equation (2) passes through (0, 3) and (1.5, 0).

Subtracting (1) from (2),

y-y=-2x+3-4x+3-6x+6=06x=6x=1

Substitute x = 1 in (1),

y=4-3=1

So intersection point of (1) and (2) is (1, 1).

Now take three points (1, 6), (0, 4) and (2, 7).

Substitute these three points in given inequality,

At (1, 6),

6>4-36>16-2+361

At (0, 4),

4>0-34>-340+343

At (2, 7),

7>8-37>57-4+37-1

Hence these three points (1, 6), (0, 4) and (2, 7) satisfy the given inequality.

Graph:

[Shaded region represents the solution set of given equality included (1, 6), (0, 4) and (2, 7)]

Algebra homework question answer, step 4, image 1

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