Linear inequalities in two variables · Short practice
Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.
Recall
Linear inequalities in two variables — objective 1
Maths4U Original · Short practice
The region R satisfies \(x\ge 2,\quad y\ge 4,\quad x+y\le 12\). All coordinates use the same length unit. Shade unwanted regions when drawing it.
Find the x-coordinate where the sloping boundary meets the horizontal boundary.
Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.
Fresh review variant
Linear inequalities in two variables — objective 1
Maths4U Original · Short practice
The region R satisfies \(x\ge 3,\quad y\ge 2,\quad x+y\le 12\). All coordinates use the same length unit. Shade unwanted regions when drawing it.
Find the x-coordinate where the sloping boundary meets the horizontal boundary.
Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.
Method
Linear inequalities in two variables — objective 2
Maths4U Original · Short practice
The region R satisfies \(x\ge 3,\quad y\ge 2,\quad x+y\le 12\). All coordinates use the same length unit. Shade unwanted regions when drawing it.
Find the y-coordinate where the sloping boundary meets the vertical boundary.
Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.
Fresh review variant
Linear inequalities in two variables — objective 2
Maths4U Original · Short practice
The region R satisfies \(x\ge 4,\quad y\ge 3,\quad x+y\le 15\). All coordinates use the same length unit. Shade unwanted regions when drawing it.
Find the y-coordinate where the sloping boundary meets the vertical boundary.
Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.
Apply
Linear inequalities in two variables — objective 3
Maths4U Original · Short practice
The region R satisfies \(x\ge 4,\quad y\ge 3,\quad x+y\le 15\). All coordinates use the same length unit. Shade unwanted regions when drawing it.
Find the area of the bounded region, in square units.
Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.
Fresh review variant
Linear inequalities in two variables — objective 3
Maths4U Original · Short practice
The region R satisfies \(x\ge 1,\quad y\ge 4,\quad x+y\le 14\). All coordinates use the same length unit. Shade unwanted regions when drawing it.
Find the area of the bounded region, in square units.
Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.
Check understanding
Linear inequalities in two variables — objective 4
Maths4U Original · Short practice
The region R satisfies \(x\ge 1,\quad y\ge 4,\quad x+y\le 14\). All coordinates use the same length unit. Shade unwanted regions when drawing it.
The line \(\displaystyle y=x\) meets the sloping boundary inside the permitted region. Find that intersection x-coordinate.
Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.
Fresh review variant
Linear inequalities in two variables — objective 4
Maths4U Original · Short practice
The region R satisfies \(x\ge 3,\quad y\ge 3,\quad x+y\le 12\). All coordinates use the same length unit. Shade unwanted regions when drawing it.
The line \(\displaystyle y=x\) meets the sloping boundary inside the permitted region. Find that intersection x-coordinate.
Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.