Simultaneous Linear Equations Solution

Surname 1
Student’s Name
Professor’s Name
Course Name
Date
Simultaneous Linear Equations
1. Solving the following pairs of simultaneous equations:
a)
x − 3y = 1
2x + 5y = 35
Using substitution method, the equations can be labeled as 1 and 2 respectively.
x − 3y = 1 (1)
2x + 5y = 35 (2)
For (1), x = 1 + 3y
Substitute this in equation 2 and solve for y
2(1+3y) +5(y) = 35
2 + 6y + 5y = 35
2+11y=35
11y=33
Y = 3
Substitute the value of y in equation 2 to solve for x
X - 3(3) = 1
X – 9 = 1

Surname 2
X = 1+9
x = 10
b)
2x + 1/3y = 1
3x + 5y = 6
Using elimination method, the two equations can be solved also.
2x + 1/3y = 1 (1)
3x + 5y = 6 (2)
Start by eliminating x by multiplying the two as follows:
3 2x + 1/3y = 1
2 3x + 5y = 6
6x + y = 3
6x + 10y = 12
-9y = -y
Y = 1
Also eliminate y by multiplying the two as follows
5 2x + 1/3y = 1
1/3 3x + 5y = 6
10x + 5/3y = 3
X + 5/3y = 2
Subtracting the two gives;
9x = 3
X = 1/3

Surname 3
c)
4x + 3y = 5
2x – 3/4y = 1
This can also be solved by elimination method as shown below:
2x + 1/3y = 1 (1)
3x + 5y = 6 (2)
Start by eliminating y by multiplying the two as follows:
-3/4 2x + 1/3y = 1
3 2x -3/4 y = 1
-3x - 9/4y = -15/4
6x- 9/4y = 3
-9x = -27/4
X = 3/4
Also eliminate x by multiplying the two as follows
2 4x + 3y = 5
4 2x – 3/4y = 1
8x + 6y = 10
8x - 3y = 4
Subtracting the two gives;
9y = 6
Y = 2/3