Explanation:
The solution set for a system of equation is the set of points where the graphs of the equations intersect.
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<h3>general case</h3>
A system will have <em>one solution</em> if there is a <em>single point of intersection</em> of the graphs of the equations.
A system will have <em>no solutions</em> if the graphs have <em>no points of intersection</em>.
A system will have an <em>infinite</em> number of <em>solutions</em> if the graphs <em>intersect at an infinite number of points</em>.
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<h3>linear equations</h3>
When the equations are linear equations, their graphs are straight lines. If the lines have different slopes, they must intersect at exactly one point: there will be one solution.
If the lines have the same slope, there are two possibilities:
- the lines are parallel -- no solutions
- the lines are coincident -- infinite solutions
The attached graph illustrates these cases.
- the red and blue lines are the graphs of a system of equations with one solution. Those lines have different slopes
- the blue and green lines are the graphs of a system of equations with no solution. Those lines are parallel.
- The red and (dotted) purple lines are the graphs of a system of equations with infinite solutions. Those lines are coincident.
Standard Form is ...
ax + by = c
where a ≥ 0, b > 0 (if a=0), and {a, b, c} are mutually prime integers (unless irrational numbers are involved).
You can get there from where you're starting in a couple of steps. Multiply by the least common denominator of any fractions. (Here, you multiply by 4.) Then put the variable terms on the opposite side from the constant term. Make sure the leading coefficient is positive.
... 4y -4 = x -12
... x -4y = 8 . . . . add 12-4y
Step-by-step explanation:
a) f(1) = -1 → x = -1
b) g(1) = Undefined
c) f(x) = 1 → x= Undefined
d) g(x) = 1 → x= 5
Answer:
The number of brownies in each batch is less than 8.
Step-by-step explanation:
Baked batches of brownies = 2.5
Number of burned brownies = 5
Number of brownies left is less than 15
So, the total number of brownies is less than 15 + 5 = 20
Number of brownies in each batch is
n < 20/2.5
n < 8
So, the number of brownies in each batch is less than 8.
Answer:
<h3 />
a. 
b. 
Step-by-step explanation:
a. Given,
Perimeter of rectangular field ( P ) = 310 m
Length of the field ( L ) = 84 m
Width of the field ( W ) = ?
<u>Finding </u><u>the </u><u>width </u><u>of </u><u>the </u><u>rectangular</u><u> </u><u>field</u>
plug the values
⇒
Distribute 2 through the parentheses
⇒
Swap the sides of the equation
⇒
Move 168 to right hand side and change it's sign
⇒
Subtract 168 from 310
⇒
Divide both sides of the equation by 2
⇒
Calculate
⇒
Width = 71 meters
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2. Given,
Area of rectangular painting ( A ) = 5185 cm²
Width of the painting ( w ) = 61 cm
Length of the painting ( l ) = ?
<u>Finding </u><u>length </u><u>of </u><u>the </u><u>painting</u>
plug the values
⇒
Swap the sides of the equation
⇒
Divide both sides of the equation by 61
⇒
Calculate
⇒
cm
Length = 85 cm
Hope I helped!
Best regards !!!
