Question

solve the following pairs of simultaneous equations

a) x=7y+3

y=3x-7

b) 2x+5y =23

5x-2y=14

Answer #1

i) Simplify the following equations 3(2x – 5) – 2(5x - 7) + 9 =
ii) Solve 3x – 2 divided by 2= 4x - 5 divided by 4 (5marks)
c) Solve the following pairs of simultaneous equations 2x + y =
7 and x - 2y = -1

Solve the system of equations given below. 2x+5y+z= -1, 3x-5y-z=
6, 5x+y+3z= 10.

Solve each system of equations
x-2y+3z=7
2x+y+z=4
-3x+2y-2z=-10

Using matrix method solve the following simultaneous
equations
3x - 1y = 7
2x + 3y = 12

(differential equations): solve for x(t) and y(t)
2x' + x - (5y' +4y)=0
3x'-2x-(4y'-y)=0
note: Prime denotes d/dt

2.Use separation of variables to solve (3x^2(1-y^2))/2y with
initial condition y(1)=2.
3.State the solution of the homogeneous ODE with roots of its
characteristic equation of r= 1,1,1,+-7i,3+-5i.
4.Consider the system of linear equations:
2x+6y+z=7
x+2y-z=-1
5x+7y-4z=9
solve this system using: a) Carmer's rule, b)Gauss-Jordan
elimination, c) an inverse matrix.

1) Solve these equations: 3x-y=-11
x+2y=8
2) Solve these equations:
x+y+z=6
x-y-z=-4
2x+y-4z=-8

Section B.3 - Algebra - Simultaneous and Quadratic Equations
Solve problems 1 and 2 using the comparison, elimination, or
substitution method.
1) x +y =2 2x -3y =5
2 ) 3x - 5y=5 7x + y = 75

Solve the system of linear equations.
3x-3y+6z=12
x+2y-z=10
5x-8y+13z=14

for 10-12 you will solve the following system of equations:
2x+y+z=-2 2x-y+3z=6 3x-5y+4z=7 10) what is the solution for x? a)2
b)-3 c)infinitely many solutions d)no solution 11) what is the
solution for y? a)2 b)0 c)inifinitely many solution d)no solution
12) what is the solution for z? a)4 b)-8 c)infinitely many
solutions d)no solutions

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