Step by step
The question
Question: is (−1, 3) a solution of 2x + y ≤ 1 and y ≥ x + 4.
① 2x + y ≤ 1 and ② y ≥ x + 4
is (−1, 3) a solution?
1 Read x and y
The first number is always x.
The second is y.
So x = −1 and y = 3.
(−1, 3) → x = −1, y = 3
Careful!
Do not swap them.
The first number in (−1, 3) is x.
Careful: not x = 3, y = −1 ✗
2 Check ①
①: Put x = −1 and y = 3 in.
2(−1) + 3 ≤? 1
Work out each side.
−2 + 3 ≤? 1
Is 1 less than or equal to 1?
Yes.
True!
1 ≤ 1 true
3 Check ②
②: Put x = −1 and y = 3 in.
3 ≥? (−1) + 4
Work out each side.
3 ≥? −1 + 4
Is 3 more than or equal to 3?
Yes.
True!
3 ≥ 3 true
Both are true.
So (−1, 3) is a solution of the system of inequalities.
(−1, 3) is a solution
Let's look back.
First: read x and y.
Then: check ①.
Last: check ②.
Answer
(−1, 3) is a solution