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2x + 2y = 5

3x + 3y = 7

How many solutions does the system of equations above have?

A. zero

B. one

C. two

D. infinitely many

**Comments**

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A system of linear equations has no solution if they are parallel when ploted on a graph.

The general form of linear equation is given as:

y = mx + c

where m is the slope and c is the intercept.

Given:

2x + 2y = 5

3x + 3y = 7

The above equations can be written in linear form as:

2x + 2y = 5

2y = -2x + 5

y = -x + 5/2 ----------- eqn(1)

and

3x + 3y = 7

3y = -3x + 7

y = -x + 7/3 ---------- eqn(2)

since both eqn(1) and eqn(2) has the same slope but different intercept, thus, both lines are parallel and has no solution

**Answer: A**

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