Question 62013: On number 1 I tried to use the calculator on the help page, but I didn't understand how they did it. And for number 2 I read what they had written as the description and read it over and over and looked in the book, but I was still lost and confused.
(1) Solve each of the following systems.
(a) x + 2y = -6
x - 2y = 14
(b) 3a - b = 0
a + 2b 7/2
(2) The equation of a straight line can be found if you are given the coordinates of two points on the line. One way to do this is to use systems of equations. The slope-intercept form for a linear equation is y = mx + b. Each point on a line must make the equation true when the coordinates are substituted for x and y. As each point is substituted, a seperate linear equation is formed; the two points produce two equations with variables m and b. Solving the system gives you the value of m and b and , thus, the equation of the line.
For each of the following pairs of points, find the line which would contain each pair.
(a) (-2, 3) and (1,9)
(b) (1/3, 2/5) and (5/3 , 1)
(c) (5, -24) and (1, 14)
(d) (3, squareroot 2) and (1, 3 sqauareroot 2)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! (1) Solve each of the following systems.
(a)
1st: x + 2y = -6
2nd: x - 2y = 14
Subtract the 1st from the 2nd to get:
-4y=20
y=-5
Substitute that into 2nd to solve for y as follows:
x-2*-5=14
x+10=14
x=4
Check in 1st as follows:
4+2(-5)=-6
4-10=-6
-6=-6
SOLUTION:
x=4,y=-5
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(b)
1st: 3a - b = 0
2nd: a + 2b =7/2
Multiply 1st be 2 to get:
3rd: 6a-2b=0
Add 2nd and 3rd to get:
7a=7/2
a=1/2
Substitute into 2nd to solve for "a", as follows:
1/2 +2b = 7/2
2b=3
b=(3/2)
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Check in 1st as follows:
3(1/2)-(3/2)=0
0=0
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(2) The equation of a straight line can be found if you are given the coordinates of two points on the line. One way to do this is to use systems of equations. The slope-intercept form for a linear equation is y = mx + b. Each point on a line must make the equation true when the coordinates are substituted for x and y. As each point is substituted, a seperate linear equation is formed; the two points produce two equations with variables m and b. Solving the system gives you the value of m and b and , thus, the equation of the line.
For each of the following pairs of points, find the line which would contain each pair.
(a) (-2, 3) and (1,9)
1st: 3=-2m+b
2nd: 9= m+b
Subtract 2nd from 1st to get:
-6=-3m
m=2
Substitute into 2nd to solve for b, as follows:
9=2+b
b=7
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Check in 1st as follows:
3=-2*2+7
3=-4+7
3=3
EQUATION:
y=2x+7
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Comment:
Follow the same procedure to find the proper
equation for the following problems.
(b) (1/3, 2/5) and (5/3 , 1)
(c) (5, -24) and (1, 14)
Cheers,
Stan H.
(d) (3, squareroot 2) and (1, 3 sqauareroot 2)
Com
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