Solve the following systems of inequalities and select the correct graph: 2x − y > 4 x + y < −1 In each graph, the area for f(x) is shaded and labeled A, the area for g(x) is shaded and labeled B, and the area where they have shading in common is labeled AB. What graph would I be using?

The "solution" is the doubly-shaded area on the graph. Here, the dashed lines cross in a sort of X pattern, and the doubly-shaded area is the quadrant at the bottom (below both lines).

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The "solution" involves graphing the boundary lines, and identifying the shaded area associated with each.

When equations are in standard form, there are a couple of different ways you can graph them. (I like to use a graphing calculator.) One way is to rewrite the equations to slope-intercept form:

y < 2x -4 . . . . . . slope of 2, y-intercept of -4, shading below the dashed line

y < -x -1 . . . . . . . slope of -1, y-intercept of -1, shading below the dashed line

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Comment on multiple choice questions

You need to identify what makes each answer choice different from the others. It might be the slopes of the lines, the y-intercepts, the side that is shaded, the nature of the line (dashed, solid). You can usually eliminate the answer choices that don't make any sense, and concentrate on the subtleties of the remaining viable candidates.

shubhamchouhanvrVT shubhamchouhanvrVT · Answer 2 · 2022-07-13T12:43:53+02:00

The "solution" is the doubly-shaded area on the graph. Here, the dashed lines cross in a sort of X pattern, and the doubly-shaded area is the quadrant at the bottom (below both lines).

What is a graph?

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The "solution" involves graphing the boundary lines and identifying the shaded area associated with each.

When equations are in standard form, there are a couple of different ways you can graph them. (I like to use a graphing calculator.) One way is to rewrite the equations to slope-intercept form:

y < 2x -4 . . . . . . slope of 2, y-intercept of -4, shading below the dashed line

y < -x -1 . . . . . . . slope of -1, y-intercept of -1, shading below the dashed line

Therefore "solution" is the doubly-shaded area on the graph. Here, the dashed lines cross in a sort of X pattern, and the doubly-shaded area is the quadrant at the bottom (below both lines).

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