Question

The value of x and y that simultaneously satisfy the equations 2x + 3y = 5 and 7x - 4y = 3 are
A. 0, 1
B. 1, 0
C. -1, 1
D. 1, 1

Answer 1

Hint: In this question remember to make any 2 real numbers of same variables in both the equations equal and then apply the subtraction or addition operation between both the operations, using this information will help you to approach towards the solution of the question.

Complete step by step answer:
According to the given information we have two different equations that are 2x + 3y = 5 and 7x - 4y = 3 .
Taking 2x + 3y = 5 as equation 1 and taking 7x – 4y = 3 as equation 2
For equation 1 multiplying it by 4 we get
4 (2x) + 4 (3y) = 4 (5)
$ \Rightarrow $8x + 12y = 20
Taking the above equation as equation 3
Now multiplying equation 2 by 3 we get
3 (7x) – 3 (4y) = 3 (3)
$ \Rightarrow $21x – 12y = 9
Taking the above equation as equation 4
Now using the addition operation between equation 4 and 3 we get
21x – 12y + 8x + 12y = 20 + 9
$ \Rightarrow $21x + 8x = 20 + 9
$ \Rightarrow $29x = 29
$ \Rightarrow $ $x = \dfrac{{29}}{{29}}$
$ \Rightarrow $x = 1
Now substituting the value of x in the equation 1 we get
2 (1) + 3y = 5
$ \Rightarrow $2 + 3y = 5
$ \Rightarrow $3y = 5 – 2
$ \Rightarrow $3y = 3
$ \Rightarrow $$y = \dfrac{3}{3}$
$ \Rightarrow $y = 1
So the value of x and y that satisfy both the equation are (1, 1)

So, the correct answer is “Option D”.

Note: In the above question was based on the concept of linear equation in two variable which can be explained as the equation which contains two variable the general representation of linear equation in two variable is given as ax + by + c = 0 here a, b and c are the integers and x and y are the two variables in the equation which means that its value is unknown, these equations have more than one solution there are more types of equations such as linear equation of one variables which have only one dissimilarities than linear equation in two variable that are linear equations with one variables consist of one variable and it consists of only one solution.