Word Problems on System of Linear Equations
Grade 8 Math Worksheets
We already know how to solve system of linear equation in one variable,
We have also discussed about system of linear equations with elimination and substitution method.
Now let us see how to solve word problems on system of linear equations.
Example: The sum of two numbers is 139 while their difference is 19. What is the larger of two numbers?
Let the two numbers be x and y.
x + y = 139 … Equation (1)
x – y = 19 … Equation (2)
Adding the two equations, we get,
2x = 139 + 19 ⇒ 2x = 158
x = 158 ÷ 2 = 79
Put this value of x in any of the two equations. Let us put in equation 1:
79 + y = 139 ⇒ y = 60
Of the two numbers 79 is the larger number.
Example: The sum of the digits of a two-digit number is 16. If 18 is added to the number, its digits are interchanged. What is the number?
Let the unit’s digit of the number be x.
Ten’s digit = 16 – x
Number = 10 × (16 – x) + x = 160 – 9x
When the digits are interchanged, number = 10x + (16 – x) = 9x + 16
160 – 9x + 18 = 9x + 16
x = 9
Ten’s digit = 16 – 9 = 7
Number = 79
- Twice a number exceeds three times another number by 6. The difference between the numbers is 7. What is the greater of the numbers?
- The perimeter of a rectangular field is 240 m. If length of the field is increased by 8 m and width is decreased by 5 m, the area of the field is decreased by 42 sq m. What is the width of the field?
- The sum of two numbers is 112. When the larger number is divided by the smaller number, the quotient is 5 and the remainder is 4. What is the smaller of the two numbers?
- The tens digit of a two digit number is three times the units digit. The sum of the number and the units digit is 32. Find the number.
- The sum of two digits in a two-digit number is 7. When the digits are interchanged the number is reduced by 9. What is the number?
- 46 meters
Personalized Online Tutoring
eTutorWorld offers affordable one-on-one live tutoring over the web for Grades 2-12, Test Prep help for Standardized tests like SCAT, CogAT, SSAT, SAT, ACT, ISEE and AP. You may schedule online tutoring lessons at your personal scheduled times, all with a Money-Back Guarantee. The first one-on-one online tutoring lesson is always FREE, no purchase obligation, no credit card required.
For answers/solutions to any question or to learn concepts, take a FREE Demo Session.
No credit card required, no obligation to purchase.
Just schedule a FREE Sessions to meet a tutor and get help on any topic you want!
Pricing for Online Tutoring
|Tutoring Package||Validity||Grade (1-12), College|
|5 sessions||1 Month||$124|
|1 session||1 Month||$25|
|10 sessions||3 months||$239|
|15 sessions||3 months||$354|
|20 sessions||4 months||$449|
|50 sessions||6 months||$1049|
|100 sessions||12 months||$2049|