QUESTION 1
The given system of equations is


To solve by linear combination, we add equation (1) to equation (2) to get,


We divide through by 4 to obtain,


We put d=3 into equation (2) to get,




QUESTION 2
The given system is
4x + y = 5 ...eqn(1)
3x + y = 3 ...eqn(2)
To solve by linear combination, we subtract equation (2) from equation (1) to eliminate y from the equation.
This will give us,

This implies that,

Put x=3 into equation (1) to get,




The solution is

QUESTION 3
We want to solve the system;
a – 2b = –2 ....eqn(1)
2a + 2b = 14...eqn(2)
by linear combination.
We need to add equation (1) to equation (2) to eliminate b.
This implies that,

Simplify,

Divide both sides by 3 to get,

Put a=4 into equation (2) to obtain,





The ordered pair in the form (a, b) is

QUESTION 4
The given system of equations is
11x + 4y = 18 ...eqn(1)
3x + 4y = 2 ...eqn(2)
We subtract equation (2) from equation (1) to get,



Put x=2 into equation (2) to obtain,

This implies that,




The correct answer is (2,-1).
QUESTION 5
The given system is ;
2d + e = 8...eqn1
d – e = 4...eqn2
We add the two equations to eliminate e.
This implies that,


We divide both sides by 3 to get,

We put d=4 into equation (2) to get,




The solution is