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Look at the system of linear inequalities.

{x−3y≤32x+5y≥10
Which graph represents the solution to the system of linear inequalities

Look at the system of linear inequalities. {x−3y≤32x+5y≥10 Which graph represents-example-1
User Dyo Medio
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Graph D represents the solution to the system of linear inequalities.

The system of inequalities is:

x - 3y ≤ 32

2x + 5y ≥ 10

We can solve this system of inequalities by graphing each inequality and then finding the region that is common to both graphs.

To graph the first inequality, x - 3y ≤ 32, we can rewrite it in y = mx + b form.

y = (1/3)x - 10

The y-intercept for the first inequality is -10. So the first line must pass through the point (0, -10).

The slope for the first inequality is 1/3. Remember that the slope tells you rise over run. So in this case for every 1 position you move up You must also move 3 positions to the right.

Graph the blue line so it passes through (0, -10) and has a slope of 1/3.

To graph the second inequality, 2x + 5y ≥ 10, we can rewrite it in y = mx + b form.

y = (-2/5)x + 2

The y-intercept for the second inequality is 2. So the second line must pass through the point (0, 2).

The slope for the second inequality is -2/5. Remember that the slope tells you rise over run. So in this case for every 2 positions you move down (because it's negative) You must also move 5 positions to the right.

Graph the green line so it passes through (0, 2) and has a slope of -2/5.

The solution to the system of inequalities is the shaded region that is common to both graphs.

The shaded region is the triangle that is bounded by the x-axis, the blue line, and the green line.

Only the graph in choice D satisfies the above conditions.

User Andrey  Yankovich
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