The coordinates below represent two linear equations. How many solutions does this system of equations have?
Line 1
x y
–2 7
0 6
Line 2
x y
3 0
0 –3
A.
0
B.
exactly 1
C.
exactly 2
D.
infinitely many
Answers
the choices:
0 solutions: means the lines don't intercect at all, meaning same slope but different y intercept or they ar paralell
1 solution: lines intercect in 1 point
2 solutions: curvy line with a straight line thorugh middle
infinetly solutions: same line
to find slope you do
slope=(y1-y2)/(x1-x2)
first line is
(2,-7)
(0,6)
(x,y)
x1=2
y1=-7
x2=0
y2=6
subsitute
(-7-6)/(2-0)=-13/2
slope=-13/2
subsitute
y=-13/2x+b
subsitute one of the points
(0,6)
x=0
y=6
6=-13/2(0)+b
6=0+b
6=b
y=-13/2+6
now solve for the other equation
(3,0)
(0,-3)
x1=3
y1=0
x2=0
y2=-3
subsitute
(0-(-3))/(3-0)=(0+3)/(3)=3/3=1
y=1x+b
subsitute
(3,0)
x=3
y=0
0=1(3)+b
0=3+b
subtract 3
-3=b
y=x-3
we have the lines
y=-13/2x-6 and
y=x-3
solve for a common solution
y=x-3 and y=-13/2x-6 therefor
x-3=-13/2x-6
add 6 to both sides
x+3=-13/2x
multiply both sides by -2
-2x-6=13x
add 2x to both sides
-6=15x
divide both sides by 15
-2/5=x
subsitute
y=x-3
y=-2/5-3
y=-3 and 2/5 or -17/5
the solution is (-2/5, -17/5)
there is only one solution
the answer is B
Related Questions
What is the gcf of 60 and 20
What is 33 over 100 in simplest form
Please solve both questions.
48% of what number is 108? A. 44.4 B. 51.84 C. 225 D. 5184
Answers
4(15) = 60
4(9+6) = 4*9 + 4*6 = 36 + 24 = 60
please hurry.
Answers
k=273.15+c
that's one of them
Answers
Answer:
B=8
Step-by-step explanation:
15² + b² = 17²
225 + b² = 289 (Subtract 289 - 225)
b² = 64 (Find the square root of 64)
√64 = 8
Answers
straight line, and any two points on it define the entire line.
-- The slope of the line is [ -a/b ] .
-- The line intersects the x-axis at [ x = c/a ] .
-- The line intersects the y-axis at [ y = c/b ] .
Answer:
-- The slope of the line is [ -a/b ] .
-- The line intersects the x-axis at [ x = c/a ] .
-- The line intersects the y-axis at [ y = c/b ] .
Step-by-step explanation:
8x = 56
8x + 16 = 40
x = 3
8x = 24
x = 7
8x – 16 = 40
8(x – 2) = 40
~~~~~~~~~~~~~~
Choose which ones to use~
Answers
Answers
Answer:
2.5 gallons are equal to 10 quarts.
Step-by-step explanation:
We know that 1 gallon is equivalent to 4 quarts.
Let's call gallons and
quarts. An expression that represents the transformation between these two units is
This expression represents the conversion factor we described at the beginning.
So, if we have 2.5 gallons, using the expression, we find the number of quarts
Therefore, 2.5 gallons are equal to 10 quarts.
The expression 2.5 gallons x 4 quarts/gallon can be used to convert 2.5 gallons into quarts.
We have,
To convert 2.5 gallons into quarts, you can use the conversion factor that states there are 4 quarts in 1 gallon.
The expression to convert 2.5 gallons into quarts would be:
2.5 gallons x 4 quarts/gallon
By multiplying 2.5 gallons by the conversion factor of 4 quarts/gallon, you would obtain the equivalent value in quarts.
Thus,
The expression 2.5 gallons x 4 quarts/gallon can be used to convert 2.5 gallons into quarts.
Learn more about expressions here:
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