Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

How do you solve 2x3y=1 and 5x+4y=14 using substitution?

Answer
VerifiedVerified
474.9k+ views
like imagedislike image
Hint: Any two linear equations can be solved to get a common point lying on their graphs. We solve these equations by addition and subtraction methods. We can solve these equations by substituting one variable after making required modifications such that any one of the variables remains in an equation. Then, we substitute the rearranged variable into the second equation and find the value of each variable.

Complete step by step answer:
As per the given question we need to solve 2x3y=1 and 5x+4y=14 to get a common point called a solution of these equations.
Let 2x3y=1 (1)
      5x+4y=14 (2)
Let us consider equation (1)
Now we add 2x on both sides to the equation (1). Then the equation becomes
2x+2x3y=12x3y=12x
Now we divide with -3 on both sides. Then the equation becomes
3y3=12x3
y=12x3 (3)
Now we substitute equation 3 in equation 2. Then the equation becomes
5x+4(12x3)=14
Now we multiply with -3 on both sides. By using distributive property, the equation becomes
5x×3+4(12x3)×3=14×3
15x+4(12x)=42
15x+48x=42
23x=46
x=4623
x=2
Now we substitute the value of x in equation 1. Then the equation becomes
2x3y=12(2)3y=1 5x×3+4(12x3)×3=14×315x+4(12x)=4215x+48x=4223x=46x=4623
43y=1
Now we add -4 on both sides then we get
443y=14
3y=3
Now we divide with -3 on both sides then we get
3y3=33
y=1
Therefore, x=2 and y=1 is the required solution.

Note:
In order to solve these types of problems, we need to have knowledge of straight lines and basic arithmetic properties. We can solve for x and y of two equations by adding them after making required modifications such that any one of the variables gets canceled. Then, we get the value of one variable. Using this we get the other variable value.