Q. 2
Show that each of the following systems of equations has a unique solution and solve it:
2x - 3y = 17, 4x + y = 13.
Answer :
Given: 2x – 3y = 17 – eq 1
4x + y = 13 – eq 2
Here,
a1 = 2, b1 = - 3, c1 = 17
a2 = 4, b2 = 1, c2 = 13
= 
, 
= 
Here, 
≠ 
∴ Given system of equations have unique solutions.
Now,
In – eq 1
2x = 17 + 3y
X = 
Substitute x in – eq 2
we get,
4× 
+ y = 13
= 13
68 + 12y + 2y = 26
68 + 14y = 26
14y = 26 – 68
14y = - 42
y = 
= - 3
∴ y = - 3
Now, substitute y in – eq 1
We get,
2x – 3×( - 3) = 17
2x + 9 = 17
2x = 17 – 9
2x = 8
x = 8/2 = 4
∴ x = 4
∴ x = 4 and y = - 3
Rate this question :
How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Dealing With the Real Life Problems53 mins
Quiz | Solution of Linear Equations53 mins
Champ Quiz | Consistency and Inconsistency of Solutions36 mins
Pair of Linear Equations in Two Variables46 mins
Smart Revision | Important Word Problems37 mins
Dealing with the Real Life Problems54 mins
Quiz | Real Life Problems Through Linear Equations56 mins
Elimination (quicker than quickest)44 mins
Bonus on Applications of Linear Equations in Two Variables43 mins
NCERT I Quiz on Solution of Linear Equations in Two Variables49 mins
Dealing With the Real Life Problems53 minsQuiz | Solution of Linear Equations53 minsChamp Quiz | Consistency and Inconsistency of Solutions36 minsPair of Linear Equations in Two Variables46 minsSmart Revision | Important Word Problems37 minsDealing with the Real Life Problems54 minsQuiz | Real Life Problems Through Linear Equations56 minsElimination (quicker than quickest)44 minsBonus on Applications of Linear Equations in Two Variables43 minsNCERT I Quiz on Solution of Linear Equations in Two Variables49 minsTry our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
view all courses
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
RELATED QUESTIONS :
Solve the following pair of linear equation by cross - multiplication method:
x + 4y + 9 = 0
5x – 1 = 3y
KC Sinha - MathematicsSolve each of the following systems of equations by using the method of cross multiplication:
2x + y = 35, 3x + 4y = 65.
RS Aggarwal - Mathematics