Maths-
General
Easy
Question
Use Substitution to solve each system of equations :
6X - 3Y = -6
Y = 2X + 2
Hint:
find x by substituting y (in terms of x) in the equation and find y by substituting value of x in the equations .If we get a true statement we say they have infinite solutions .If we get the false statement we say they have no solution.
The correct answer is: They have infinite no.of solutions for the given system of equations
Ans :- infinite no.of solutions .
Explanation :-
y = 2x + 2— eq 1
6x - 3y = -6—- eq 2
Step 1 :- find x by substituting y = 2x + 2 in eq 2.
6x - 3 (2x + 2) = -6 ⇒ 6 x -6x - 6 = -6
-6 = -6
Here we get -6 = -6 which is always true i.e always having a root .
They coincide with each other and have infinite no.of solutions
They have infinite no.of solutions for the given system of equations
Related Questions to study
Maths-
Given: 𝑚∠𝑃 = 30°, 𝑚∠𝑄 = 30° , 𝑚∠𝑄 = 𝑚∠𝑅
Prove: 𝑚∠𝑃 ≅ 𝑚∠𝑅 = 30°
Given: 𝑚∠𝑃 = 30°, 𝑚∠𝑄 = 30° , 𝑚∠𝑄 = 𝑚∠𝑅
Prove: 𝑚∠𝑃 ≅ 𝑚∠𝑅 = 30°
Maths-General
Maths-
Use the given information and the diagram to prove the statement.
Given: 𝑚∠𝑃𝑀𝐶 + 𝑚∠𝑃𝑀𝐷 = 180° and 𝑚∠𝑃𝑀𝐶 = 150°
Prove: 𝑚∠𝑃𝑀𝐷 = 30°
Use the given information and the diagram to prove the statement.
Given: 𝑚∠𝑃𝑀𝐶 + 𝑚∠𝑃𝑀𝐷 = 180° and 𝑚∠𝑃𝑀𝐶 = 150°
Prove: 𝑚∠𝑃𝑀𝐷 = 30°
Maths-General
Maths-
Solve the system of equations by elimination :
3X + 2Y = 8
X + 4Y = - 4
Solve the system of equations by elimination :
3X + 2Y = 8
X + 4Y = - 4
Maths-General
Maths-
Give a two-column proof.
Given:
Prove: PR = 25 in
Give a two-column proof.
Given:
Prove: PR = 25 in
Maths-General
Maths-
Use Substitution to solve each system of equations :
- 3X - Y = 7
X + 2Y = 6
Use Substitution to solve each system of equations :
- 3X - Y = 7
X + 2Y = 6
Maths-General
Maths-
If Q is the midpoint of PR, prove that PR = 2 PQ.
Give a two-column proof.
If Q is the midpoint of PR, prove that PR = 2 PQ.
Give a two-column proof.
Maths-General
Maths-
Compare 𝑚∠𝑃𝑂𝑄𝑎𝑛𝑑∠𝑆𝑂𝑇.
Compare 𝑚∠𝑃𝑂𝑄𝑎𝑛𝑑∠𝑆𝑂𝑇.
Maths-General
Maths-
Which postulate will you use to prove that PR = PQ + QR?
Which postulate will you use to prove that PR = PQ + QR?
Maths-General
Maths-
Solve the system of equations by elimination :
X - 2Y = - 2
3X + 2Y = 30
Solve the system of equations by elimination :
X - 2Y = - 2
3X + 2Y = 30
Maths-General
Maths-
Solve the following by using the method of substitution
Y = 4X+2
Y = X+8
Solve the following by using the method of substitution
Y = 4X+2
Y = X+8
Maths-General
Maths-
If lines l and m are parallel, find the value of x.
If lines l and m are parallel, find the value of x.
Maths-General
Maths-
Prove that: PR = PQ + QR
Give a two-column proof
Prove that: PR = PQ + QR
Give a two-column proof
Maths-General
Maths-
Find x and hence find 𝑚∠𝐶𝑂𝐷
Find x and hence find 𝑚∠𝐶𝑂𝐷
Maths-General
Maths-
Solve the system of equations by elimination :
X - Y = 4
2X + Y = 5
Solve the system of equations by elimination :
X - Y = 4
2X + Y = 5
Maths-General
Maths-
Use Substitution to solve each system of equations :
X = -Y + 3
3X - 2Y = -1
Use Substitution to solve each system of equations :
X = -Y + 3
3X - 2Y = -1
Maths-General
