Question

A set of equations is given below:

Equation C: y = 4x + 8
Equation D: y = 4x + 2

Which of the following best describes the solution to the given set of equations?

No solution
One solution
Two solutions
Infinitely many solutions

Answer 1

There is no solution.

Explanation:

Answer 2

The answer is: [A]: "No solution" .
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Note: Given:
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y = 4x + 8 ;
y = 4x + 2 ;
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Since: "y = y" ;

4x + 8 = 4x + 2 ; which is not true;
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4x + 8 ≠ 4x + 2 ; since, "8 ≠ 2" ;

Note: Suppose: "4x + 8 = 4x + 2" ;

→ Subtract "4x" from each side of the equation:

4x + 8 − 4x = 4x + 2 − 4x ;

to get:
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" 8 = 2 " ; not true ; since "8 ≠ 2" ;
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Also, suppose:
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4x + 8 = 4x + 2 ;

→ Subtract "2" from BOTH SIDES of the equation;

4x + 8 − 2 = 4x + 2 − 2 ;

to get:

4x + 6 = 4x

(Note: "4x + 0 = 4x" ; but "4x + 6 ≠ 4x") l

But even if we have:

4x + 6 = 4x ;

→ Subtract "4x" from EACH side of the equation:

4x + 6 − 4x = 4x − 4x ;

to get:

6 = 0 ; which is not true; "6 ≠ 0" .
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The correct answer is: [A]: "No solution" .
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