Hello Yahoo Answers world have a few more math questions, Help confused, I forgot how to do these, look.......

Question

4. Solve the system of equations using the substitution method.
If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is “no solution” or “infinitely many solutions.”
-3x + y = 1
5x + 2y = -4




5. Solve the system of equations using the addition (elimination) method.
If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is “no solution” or “infinitely many solutions.”
-7x + y = 8
2x – y = 2




6. Solve the system of equations using the addition (elimination) method.
If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is “no solution” or “infinitely many solutions.”
3x – 2y = -7
-9x + 6y = 21

Thank you for the help in advance yahoo answers community!


1. Find the slope of the line that passes through the points (2, 3) and (5, 8).




2. Find the equation of the line that passes through the points (3, -2) and (4, -2).




3. Find the equation, in standard form, with all integer coefficients, of the line perpendicular to x + 3y = 6 and passing through (-3, 5).

Answer 1

4.
-3x + y = 1
5x + 2y = -4

Place the first in terms of y:

y = 1 + 3x

Substitute "1 + 3x" for "y" in the second equation:

5x + 2y = -4
5x + 2(1+3x) = -4
5x + 2 + 6x = -4
11x = -6
x = -6/11

Substitute that value back into either original equation to solve for y:

-3x + y = 1
-3 (-6/11) + y = 1
18/11 + y = 1
y = -7/11

(-6/11, -7/11)

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5.
-7x + y = 8
2x – y = 2

Add the two equations vertically

-7x + y = 8
2x – y = 2
---------------
-7x + 2x + y - y = 2 + 8

Combine like terms to cancel out y and solve for x:

-5x = 10
x = -2

Substitute back into either original equation to solve for y:

2x - y = 2
2(-2) - y = 2
-4 - y = 2
y = -6

(-2,-6)

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6.
3x – 2y = -7
-9x + 6y = 21

Multiply the first equation by -3 to match up the coefficients of x:

3x – 2y = -7
-9x + 6y = 21

-3(3x) - (-3)2y = -3(-7)
-9x + 6y = 21

-9x + 6y = 21
-9x + 6y = 21

Both are the same equation. The answer is therefore every point on the line defined by either equation (since they both define the same line), and "infinitely many solutions."