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Maths-

SAT

Easy

Question

What system of linear equations is represented by the lines shown?

3x - 2y = 6 3x- 2y=12
3x - 2y = 6 3x+2y=12
2x + 3y = 6 2x-3y=12
-2x -3y = 6
- 2x + 3y = 12

The correct answer is: 3x - 2y = 6
3x- 2y=12

The first passes through (2,0) & (0,-3)
The equation of line is
$fraction numerator y minus y subscript 1 over denominator y subscript 2 minus y subscript 1 end fraction equals fraction numerator x minus x subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction fraction numerator y minus 0 over denominator negative 3 minus 0 end fraction equals fraction numerator x minus 2 over denominator 0 minus 2 end fraction y over 3 equals fraction numerator x minus 2 over denominator 2 end fraction 2 y equals 3 x minus 6 3 x minus 2 y space equals space 6$
The second passes through (0,-6) & (4,0)
The equation of line is
$fraction numerator y minus y subscript 1 over denominator y subscript 2 minus y subscript 1 end fraction equals fraction numerator x minus x subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction fraction numerator y plus 6 over denominator 0 plus 6 end fraction equals fraction numerator x minus 0 over denominator 4 minus 0 end fraction fraction numerator y plus 6 over denominator 6 end fraction equals x over 4 4 y space plus space 24 space equals 6 x 6 x space minus space 4 y space equals space 24 3 x space minus space 2 y space equals space 12$

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