Question

Please help me with this!
Choose the right system for each equation(picture)
Picture one: Inconsistent, consistent, or equivalent?
Picture two: Inconsistent, consistent, or equivalent?
picture three: Inconsistent, consistent, or equivalent?
picture four: Inconsistent, consistent, or equivalent?
picture five: Inconsistent, consistent, or equivalent?

Answer 1

1.  The first equation is - 2x + 5y = 0

Second equation is $y = \frac{2}{5} x$

5y = 2x

- 2x + 5y = 0

Hence, the two equations are equivalent.

2.  $a_{1} = 2, a_{2} = - 2$

$b_{1} = -1,  b_{2} = -1$

$\frac{a_{1} }{a_{2}} =\frac{2}{-2} = -1$

$\frac{b_{1} }{b_{2}} = \frac{-1}{-1}  = 1$

$\frac{a_{1} }{a_{2}} \neq \frac{b_{1} }{b_{2}}$

Hence, the equations are consistent.

3.   $a_{1} = 4, a_{2} = 6$

$b_{1} = -1, b_{2} = -1$

$\frac{a_{1} }{a_{2}} =\frac{4}{6} = \frac{2 }{3}$

$\frac{b_{1} }{b_{2}} = \frac{-1}{-1} = 1$

$\frac{a_{1} }{a_{2}} \neq \frac{b_{1} }{b_{2}}$

Hence, the equations are consistent.

4.  Equations can be re-arranged as:

x + y - 4 = 0 and

x + y + 6 = 0

$a_{1} = 1, a_{2} = 1$

$b_{1} = 1, b_{2} = 1$

$c_{1} = -4, c_{2} = 6$

$\frac{a_{1} }{a_{2}} =\frac{1}{1} = 1$

$\frac{b_{1} }{b_{2}} =\frac{1}{1} = 1$

$\frac{c_{1} }{c_{2}} =\frac{-4}{6} = \frac{-2}{3}$

$\frac{a_{1} }{a_{2}} = \frac{b_{1} }{b_{2}} \neq \frac{c_{1} }{c_{2}}$

Hence, the equations are inconsistent.

5.  If we multiply the first equation by 4, we will get,

2y = -4x + 20 which is the second equation.

Hence, the equations are equivalent.

Answer 2

pic 1: equivalent

pic 2 : consistent

pic 3: consistent

pic 4: inconsistent

pic 5: equivalent.

number 6 incase you have it y=3x-2, 3x-y=4 :inconsistent

Step-by-step explanation:

consistent means they share a point, equivalent is when they have infinite or many touching points so basically the same line. And inconsistent means no sharing points so two different lines.