Consistent means 1 solution
inconsistent means no solutions....because they are parallel lines
equivalent means infinite solutions...because they are the same line
y = 3x - 2 3x - y = 4
-y = -3x + 4
y = 3x - 4
both equations have the same slope but different y intercepts....this means they are parallel lines and have no solutions ....INCONSISTENT
=======================
1/2y = -x + 5 2y = -4x + 20
y = -2x + 10 y = -2x + 10
same equation.....same line...infinite solutions...EQUIVALENT
===================
y = -x + 4 x = -y - 6
y = -x - 6
same slope, different y intercepts....parallel lines......no solutions...this means INCONSISTENT
==================
y = 4x + 2 y = 6x - 10
different slopes, different y intercepts...one solution...CONSISTENT
==================
y = 2x + 1 y = -2x + 3
different slopes, different y intercepts...one solution...CONSISTENT
=================
-2x + 5y = 0 y = 2/5x
5y = 2x
y = 2/5x
same line....infinite solutions....EQUIVALENT
Step-by-step explanation:
Rearrange the terms by writing
3y = -2x + 6 ---> y = (-2/3)x + 2
The slope of this equation is m = -2/3
Answer:
<h2>The lengths of the bases of the trapezoid:</h2><h2>
42/h cm and 84/h cm.</h2>
Step-by-step explanation:
The formula of an area of a triangle:
<em>b</em><em> </em>- base
<em>h</em> - height
We have <em>b = 21cm, h = 6cm</em>.
Substitute:
The formula of an area of a trapezoid:
<em>b₁, b₂</em> - bases
<em>h</em><em> - </em>height
We have <em>b₁ = 2b₂</em>, therefore <em>b₁ + b₂ = 2b₂ + b₂ = 3b₂</em>.
The area of a triangle and the area of a trapezoid are the same.
Therefore
<em>multiply both sides by 2</em>
<em>divide both sides by 3</em>
<em>divide both sides by h</em>
Answer:
x=1
Step-by-step explanation:
Use the distributive property on 2(4x - 4), which makes the equation 3x+8x-8=3
Simplify, which makes the equation 11x-8=3
Add 8 to both sides, which makes the equation 11x=11
Divide both sides by 11, which makes the equation x=1
