ANSWER
1. A
2. C
3. D
4. B
5. E
EXPLANATION
QUESTION A
The given system of equation is :
[tex]x-4y=-8...(1)[/tex]
and
[tex]2x-3y=-16...(2)[/tex]
Make x the subject in equation (1)
This implies that;
[tex]x=4y-8...(3)[/tex]
Put equation(3) into equation (2).
[tex]2(4y-8)-3y=-16[/tex]
[tex]8y-16-3y=-16[/tex]
Group like terms;
[tex]8y-3y=-16+16[/tex]
[tex]5y=0[/tex]
[tex]y=0[/tex]
Put y=0 into equation(3).
[tex]x=4(0)-8[/tex]
[tex]x=-8[/tex]
(-8,0)
QUESTION B
First equation: [tex]x-y=-2[/tex]
Second equation: [tex]3x-y=0[/tex]
Subtract the first equation from the second equation.
[tex]3x-x-y+y=0+2[/tex]
Simplify;
[tex]2x=2[/tex]
[tex]x=1[/tex]
Put x=1 into any of the equations, say the first one.
[tex]1-y=-2[/tex]
[tex]-y=-2-1[/tex]
[tex]-y=-3[/tex]
[tex]y=3[/tex]
(1,3)
QUESTION C
First equation: [tex]x+y=-4[/tex]
Second equation: [tex]-3x+2y=2[/tex]
Make y the subject in the first equation;
[tex]y=-x-4[/tex]
Put y=-x-4 into the second equation;
[tex]-3x+2(-x-4)=2[/tex]
Expand:
[tex]-3x-2x-8=2[/tex]
Group like terms:
[tex]-3x-2x=2+8[/tex]
[tex]-5x=10[/tex]
[tex]x=-2[/tex]
Put x=-2 into [tex]y=-x-4[/tex]
This implies that;
[tex]y=--2-4[/tex]
[tex]y=-2[/tex]
(-2,-2)
QUESTION D
First equation:4x+6y=-12
Second equation: 2x+3y=9
Divide the first equation by 2;
New equation: 2x+3y=-6
Subtract the second equation from the new equation;
[tex]2x-2x+3y-3y=-6-9[/tex]
[tex]0=-18[/tex]. This statement is not true.
The system has no solution;
QUESTION E
First equation: [tex]x+y=-1[/tex]
Second equation: [tex]4x+4y=-4[/tex]
Divide the second equation by 4;
New equation: [tex]x+y=-1[/tex]
Subtract the second equation from the new equation;
[tex]x-x+y-y=-1+1[/tex]
[tex]\Rightarrow 0=0[/tex] This statement is true.
This system has infinitely many solutions.
