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Algebra
quiz : solutions for systems
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Terms in this set (28)
3x + 2y = 6
4x + y = 1
Solve the system of equations.
(-4/5, 21/5)
Solve the linear system.
x + y = -3
y = 2x
(-1, -2)
Find the slope of the line that passes through the points (2, 1) and (-4, -5).
1
Given two lines:
5x + 2y = 6
3x - ay = 4
Which value of a makes given lines parallel to each other?
-6/5
Find the slope of the line that passes through the points (0, 0) and (-2, -3).
2/3
The slope of the line whose equation is 3y + 2x = 1 is
-2/3
The slope of the line whose equation is y - 3 = 0 is
no slope
2x + y = 8
x + y = 4
The lines whose equations are given intersect at
(4, 0)
Which of the following points is collinear with (2, 1) and (3, 3)?
(1, -1)
(i guessed on this one)
Write the standard form of the line that is parallel to 2x + 3y = 4 and passes through the point (1, -4). Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.
Slope of the equation= -2/3
as the new line is parallel to the equation,
it's slope also equals to -2/3
(y+4)/(x-1)= -2/3
3y+12=-2x+2
ans:2x+3y+10=0
Jane says that she can use addition to show that the graphs of 2x - 3y = 1 and 2x + 3y = 2 are intersecting lines. In two or more complete sentences, describe the process of using addition to show that the lines are intersecting.
Two lines in a plane can intersect ,overlap or be parallel.When two lines intersect they have a common point which lies on both line .This is called solution of the two simultaneous equation which when graphed represent straight lines. Adding the two equations uses Elimination method to solve for x and y. The x and y value obtained is the common point lying on both the lines.
2x - 3y = 1
+ 2x + 3y = 2
---------------------
4x =3 Or x= [\frac{3}{4} .]
Substituting x value in any of the two equation we can find corresponding y value .
2x-3y=1
[2 (\frac{3}{4} ) -3y=1]
Solving for y
y= [\frac{1}{6} .]
The point of intersection of the two lines is ( [(\frac{3}{4} ,\frac{1}{6} )]
x + y = 6
x - y = 8
Solve the system of equations.
(7, -1)
Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite.
x + y = 6
x - y = 0
one solution
Write the equation of the line that passes through the given points. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.
(2, 3) and (2, 5)
2x - 3y = - 13
the equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
First obtain the equation in slope-intercept form
y = mx + c ( m is the slope and c the y-intercept )
calculate m using the gradient formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (1, 5 ) and (x₂, y₂ ) = (- 2, 3 )
m = [\frac{3-5}{-2-1}] = [\frac{-2}{-3}] = [\frac{2}{3}]
y = [\frac{2}{3}] x + c ← partial equation
to find c substitute either of the 2 points into the partial equation
using (1, 5 ), then
5 = + c ⇒ c =
rearrange the equation into standard form
multiply through by 3
3y = 2x + 13 ( subtract 3y and 13 from both sides )
2x - 3y = - 13 ← in standard form
Write the standard form of the line that contains a slope of and passes through the point (1, 1). Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.
By definition, the generic equation of the line is given by:
y-yo = m (x-xo)
Where,
(xo, yo): ordered pair where the line passes
m: slope of the line
For this case we have:
(xo, yo) = (1, 1)
Suppose that m is the value of the slope.
Substituting values we have:
y-1 = m (x-1)
Rewriting the equation in its standard form we have:
y = mx + (1-m)
3x + 2y = 5
5x + 2y = 7
Based on the given system of equations, which of the following is not true?
8x = 12
Write the slope-intercept form of the line with a slope of 2 and a y-intercept of -4. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.
Y= 2x-4 is the slop-intercept form your'e looking for there isn't a lot of work include because you;re just plugging what you have in the equation y=bx+m
Write the standard form of the line that passes through the given points. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.
(4, 7) and (0, 7)
(4,7)(0,7)...notice how the y values are the same....this means that the line is horizontal line with a 0 slope and is represented by y = a number. That number is the number in the y value....so ur equation is y = 7.....or y = 0x + 7....because the slope, in y = mx + b form, is in the m position.
y = 0x + 7....but we need it in standard form : Ax + By = C
0x + y = 7 <== standard form
The slope of the line whose equation is 2x - 1 = 0 is
no slope
Ben has $3.40 consisting of quarters and dimes. How many coins of each kind does he have if he has 22 coins?
Which of the following system of equations represents the word problem if d is the number of dimes and q is quarters?
d + q = 22 and 10d + 25q = 340
The slope of the line whose equation is 3x - 2y = 4 is
3/2
The y-intercept of the line whose equation is 3x + 2y = 7
7/2
Write the standard form of the line that has a slope of - and y-intercept of -2. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.
3x + 4y = - 8
The equation of a line in standard form is Ax + By = C
where A is a positive integer and B, C are integers
Express the line in ' slope- intercept form '
y = mx + c → (m is the slope and c is the y-intercept)
here m = - and c = - 2
hence y = - x - 2 → equation in slope- intercept form
multiply all terms by 4
4y = - 3x - 8
add 3x to both sides
3x + 4y = - 8 → in standard form
6x - 2y = 5
3x - y = 10
Solve the system of equations.
no solution
Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite.
x + 2y = 0
2x + 4y = 0
no solution
Given two lines:
3x + y = 1
bx - y = 3
Which value of b makes the given lines parallel to each other?
-3
2x - 6y = 5
x + y = 2
Solve the system of equations.
(17/8, -1/8)
Write the standard form of the line that passes through the given points. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.
(3, 1) and (-2, 3)
The equation of a line passing through (a,b) and (c,d) is given by :_
[(y-b)=\dfrac{d-b}{c-a}(x-a)]
Then, the equation of a line passing through (3, 1) and (-2, 3) is given by :-
[(y-1)=\dfrac{3-1}{-2-3}(x-3)\\\\\Rightarrow\ (y-1)=\dfrac{2}{-5}(x-3)\\\\\Rightarrow\ -5(y-1)=2(x-3)\\\\\Rightarrow\ -5y-5=2x-6\\\\\Rightarrow\ 2x+5y-6+5=0\\\\\Rightarrow\ 2x+5y-1=0]
Hence, the equation of the kine in standard form = [2x+5y-1=0]
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