Exploration: Solving a System of Inequalities

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6 questions

Systems of linear inequalities
● What does it mean to be linear?
● How do the gradients of different lines demonstrate the
relationship between them?
A system of inequalities has more than one variable and more than one inequality that are all true simultaneously.

Graph the system of equations y = x + 1 and y = 4 - 2x and label their point of intersection clearly.

Choose a point on your coordinate grid. Substitute the x and y values for
this point into the two equations. Determine if they satisfy the inequality
y ≤ x + 1. Choose more points until you have identiffied the region of
the graph that contains the set of points that satisfy y ≤ x + 1. Shade this
region of the graph.

Repeat step 2 to find and shade the region of the graph where the points
satisfy the inequality y ≥ 4 - 2x

On your graph, find the region that satisfies both inequalities y ≤ x + 1
and y ≥ 4 - 2x. Test some points in the region.

Determine how you would modify your graph if you had y < x + 1 and
y > 4 2x instead of y ≤ x + 1 and y ≥ 4 - 2x. State whether or not the
solution set would be the same.

Reflect: Why do you think that you have learned how to find the solution set
for a system of linear inequalities graphically rather than algebraically?

Exploration: Solving a System of Inequalities

Graph the system of equations y = x + 1 and y = 4 - 2x and label their point of intersection clearly.

Repeat step 2 to find and shade the region of the graph where the pointssatisfy the inequality y ≥ 4 - 2x

On your graph, find the region that satisfies both inequalities y ≤ x + 1and y ≥ 4 - 2x. Test some points in the region.

Determine how you would modify your graph if you had y < x + 1 andy > 4 2x instead of y ≤ x + 1 and y ≥ 4 - 2x. State whether or not thesolution set would be the same.

Reflect: Why do you think that you have learned how to find the solution setfor a system of linear inequalities graphically rather than algebraically?

Repeat step 2 to find and shade the region of the graph where the points
satisfy the inequality y ≥ 4 - 2x

On your graph, find the region that satisfies both inequalities y ≤ x + 1
and y ≥ 4 - 2x. Test some points in the region.

Determine how you would modify your graph if you had y < x + 1 and
y > 4 2x instead of y ≤ x + 1 and y ≥ 4 - 2x. State whether or not the
solution set would be the same.

Reflect: Why do you think that you have learned how to find the solution set
for a system of linear inequalities graphically rather than algebraically?