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

Find the solution for the system of equations 2x+y=10 and 5xy=18 .

Answer
VerifiedVerified
461.4k+ views
like imagedislike image
Hint: The equation given in the question has two variables “x” and “y” that are linear equations in two variables. These are also called simultaneous equations also known as systems of equations that contain multiple variables. These equations can be solved by methods like substitution method, elimination method.

Complete step-by-step answer:
When one variable can be easily isolated in one of the two equations then this can be solved as a substitution method. The first equation should be solved for one variable. The solved equation should be substituted into the second equation.
Hence solving the first equation for “y” we have,
 2x2x+y=102x0+y=102xy=102x
Now substituting 102x for “y” in the second equation and solving for “x” we have,
 5x(102x)=18
Expanding the brackets by multiplying the negative sign we have,
 5x10+2x=187x10=18
Adding 10 both the sides in left hand side and right hand side we have,
 7x10+10=18+107x0=287x=28
Dividing by 7 ,
 7x7=287
Cancelling 7 and dividing 7 by 28 ,
 x=4
Now substituting 4 for “x” in the solution to the first equation and calculating for “y” we have,
 y=10(2×4)y=108y=2
So, the correct answer is “x = 4 and y = 2”.

Note: The solution should be tested by substituting into both the equations and making sure that the equations hold true. The solution should be substituted for the second variable back into the first equation and should be solved for the first variable. Mathematically a solution is simply a pair of points that make a series of equations true. Graphically represented, a solution is a series of points where the lines of the equations intersect.
Latest Vedantu courses for you
Grade 10 | MAHARASHTRABOARD | SCHOOL | English
Vedantu 10 Maharashtra Pro Lite (2025-26)
calendar iconAcademic year 2025-26
language iconENGLISH
book iconUnlimited access till final school exam
tick
School Full course for MAHARASHTRABOARD students
PhysicsPhysics
BiologyBiology
ChemistryChemistry
MathsMaths
₹34,650 (9% Off)
₹31,500 per year
Select and buy