Solve each system by substitution. ????? I NEED HELP?

Question

Solve each system by substitution. Determine whether the equations are independent, dependent or inconsistent.

y= -3x + 19

y = 2x - 1

separate question

y = -4x - 7

y = 3x

separate question

y = x + 4

3y - 5x = 6

separate question

2x - y = 4

2x - y =3

separate question

x + 3y = 2

-x + y = 1

Answer 1

Take the first case and substitute y from the second equation to the first.

You get:

2x - 1 = -3x +19......(1), and

5x = 20

x = 4 => y = 7.

etc.

Equations are dependent iff in eq (1) left side equals to the right side (so you couldn't find x). Equations are inconsistent iff in eq (1) coefficient with x cancels and left side is different from the right side.

For instance your forth case  are inconsistent since replacing y from the first into the second gives:

2x - 3 = 2x - 4 => 3 = 4 inconsistent.

However if the second equation was 4x - 2y = 8 then replacing y from the first into the second would give:

4x - 2(2x - 4) = 8 => 8 = 8 => dependent.

Answer 2

2x - 1= -3x + 19

5x = 20

x = 4

y = 7

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3x = -4x - 7

7x = -7

x = -1

y = can't get this answer, equation is inconsistent

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y = x + 4

3(x+4) - 5x = 6

3x + 12 - 5x = 6

-2x + 12 = 6

-2x = - 6

x = 3

y = 7

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2x - y = 4

2x - y =3  obviously inconsistent

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you try the last one!!!