SOLVING SIMULTANEOUS EQUATIONS ALGEBRAICALLY WORKSHEET

Find the simultaneous solution of the following pairs of equations using an algebraic method:

Problem 1 :

y = x + 1

y = 2x - 3

Solution

Problem 2 :

y = x + 4

y = -x + 2

Solution

Problem 3 :

y = x + 2

y = -2x + 5

Solution

Problem 4 :

y = -2x - 4

y = x - 4

Solution

Problem 5 :

y = -x + 4

y = 2x - 8

Solution

Problem 6 :

y = 2x + 3

y = 2x - 2

Solution

Problem 7 :

y = 3x + 7

y = -x - 6

Solution

Problem 8 :

y = -2x + 3

y = -2x + 6

Solution

Problem 9 :

y = 5 - 3x

y = 10 - 6x

Solution

Problem 10 :

-15x + 3y = 12

y + 132 = x² - 4x

The graphs of the given equations in the xy-plane intersect at the point (x, y). What is the possible value of x..

Solution

Problem 1 :

The sum of two consecutive even integers is ninety-four. Find the numbers.

Solution

Problem 2 :

One hundred sixty-two guests attended a banquet. Three servers provided their beverages. The first server helped three times as many people as the second server and the third server helped twice as many people as the first server. How many guests did each server help?

Solution

Problem 3 :

The sum of three numbers is fifty-eight. The second number is four more than the first number and the third number is eight more than the second number. What are the numbers?

Solution

Problem 4 :

Two case workers share an office. The first case worker has fifteen active cases. The second case worker has twice the number of active cases. How many active cases does the office have?

Solution

Problem 5 :

Nine times a number decreases by five is equal to forty-nine. What is the number?

Solution

Problem 6 :

The sum of two consecutive integers is one hundred twenty-three. Find the two numbers.

Solution

Problem 7 :

A college has two depositional systems classes with a total of two hundred thirty-seven students. One class has forty-five more students than the other class. How many students are in each class?

Solution

Problem 8 :

If 3 is subtracted from 3 times the number x, the result is 21. What is the result when 8 is added to half of x ?

Solution

Problem 9 :

Marcia basked 240 cookies and distributed a third of them evenly among c class mates. Each classmates received 4 cookies. Which equation represent this situation ?

a) 3c/240 = 4            b) 240c/3 = 4

c)  240/3c = 4            d) 240(3)/c = 4

Solution

Problem 10 :

Point B lies on line segment AC such that the length of AB is 7 more than twice the length of BC. If the length of AC is 55. What is the length of AB ?

Solution

Solve the following pairs of simultaneous equations:

Problem 1 :

2x + 1/3y = 1

3x + 5y = 6

Solution

Problem 2 :

4x + 3y = 5

2x - 3/4y = 1

Solution

Problem 3 :

1/3x + y = 10/3

2x + 1/4y = 11/4

Solution

Problem 4 :

3x - 2y = 5/2

1/3x + 3y = -4/3

Solution

Problem 5 :

x = 1/3y

2y - 6x = 9

Solution

Problem 6 :

(4/3) + (5x/4) = 28y + (5x/8)

my = (1/2)(5x - 8)

In the given system of equations, m is a constant. If the system has no solution. What is the value of m ?

Solution

Problem 7 :

If (x + y)/x = 9 and ay/3x = 32 where a is a constant. What is the value of a ?

Solution

Problem 8 :

mx - 6y = 10

2x - ny = 5

In the given system of equations m and n are constants. The system has infinitely many solutions. What is the value m/n ?

a)  1/12      b)  1/3      c)  4/3     d)  3

Solution