
Linear Equation
Authored by MUHAMMAD FAIZ BIN SHAIRUL AZMAN STUDENT
Mathematics
8th Grade
Used 1+ times

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5 questions
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1.
OPEN ENDED QUESTION
3 mins • 1 pt
Verify that x = 4 is the root of the equation 3x/2 = 6
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Answer explanation
To verify whether the given root is the solution of the given equation, substitute x = 4 in the equation 3x/2 = 6.
⇒ (3(4))/2 = 6
⇒ (12/2) = 6
⇒ 6 = 6
Hence, x = 4 is the root of the equation 3x/2 = 6.
2.
OPEN ENDED QUESTION
3 mins • 1 pt
If x = 2, then 2x – 5 = 7. Check whether the statement is true or false?
Evaluate responses using AI:
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Answer explanation
Given equation: 2x – 5 = 7
If x = 2,
= 2(2) – 5
= 4 – 5 = -1
Hence, the given statement is false
3.
OPEN ENDED QUESTION
3 mins • 1 pt
Express the equation x = 3y in the form of ax+by+c = 0 and find the values of a, b and c ?
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Answer explanation
Given equation: x = 3y
We know that the standard form of linear equation in two variables is ax+by+c = 0 …(1)
Now, rearranging the given equation, we get
⇒ x – 3y = 0
This can be written as
⇒ 1(x) + (-3)y + (0)c = 0 …(2)
On comparing equation (1) and (2), we get
⇒ a = 1, b = -3 and c = 0.
4.
OPEN ENDED QUESTION
3 mins • 1 pt
Find three solutions for the equation 2x + y = 7.
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Answer explanation
To find the solutions for the equation 2x + y = 7, substitute different values for x.
When x = 0,
⇒ 2(0) + y = 7
⇒ y = 7
Therefore, the solution is (0, 7).
When x = 1,
⇒ 2(1) + y = 7
⇒ y = 7 – 2
⇒ y = 5
Hence, the solution is (1, 5).
When x = 2,
⇒ 2(2) + y = 7
⇒ 4 + y = 7
⇒ y = 3
Hence, the solution is (2, 3).
Therefore, the three solutions are (0, 7), (1, 5) and (2, 3).
5.
OPEN ENDED QUESTION
3 mins • 1 pt
Solve the following equations using the substitution method:
3x + 4y = 10 and 2x – 2y = 2
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Answer explanation
3x + 4y = 10 …(1)
2x – 2y = 2 …(2)
Equation (2) can be written as:
2(x – y) = 2
x – y = 1
x = 1+y …(3)
Now, substitute (3) in (1), we get
3 (1+y) + 4y = 10
3 + 3y + 4y = 10
7y = 10 – 3
7y = 7
Hence, y = 1.
Now, substitute y = 1 in (3), we get
x = 1 + 1
x = 2.
Hence, x = 2 and y = 1 are the solutions of the given equations.
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