Algebra not my subject?

Question

Solve the system of equations using addition elimination method. . If the answer is a unique solution, present it was an ordered pair (x,y)

If not, specify whether the answer is no solution of infinitely many solutions

3x -2y = -7

-9x + 6y =21

Show all work

Answer 1

#1: 3x -2y = -7
#2: -9x + 6y =21

Multiply #1 by 3... (that will give you 9x so we can eliminate the x values...)

#1: 9x - 6y = -21

Now add that to #2:
(9x - 6y) + (-9x + 6y) = -21 + 21
0 = 0

Because we got 0 = 0, that tell us there are infinite solutions in this case because the two equations are for the exact same line.

Answer 2

The addition elimination method is when you multiply an equation by any number (except zero) so that you get the coefficients to be the same (with opposite signs) for the x's or the y's so that when you add the two equations together, you will eliminate either the x's or the y's (sometimes both).
Let's say you choose to eliminate x here. notice the top is 3x and the bottom one is -9x. So what do you need to multiply the top one by to get 9x? 3! so multiply everything in the top equation by 3 to get:
9x-6y=-21 and add it to the bottom equation to get
0=0. 0=0 is a CONSISTENT system of equations and this means the two equations are of the exact same line. These are always the trickiest ones for my students to answer. You can answer it in two ways:
Pick EITHER of the two equations (cause they're both the same) and either
A) solve for x to get: x=2/3y-7/3. in this case this is what x equals, but since you don't know what y is, it's called a parameter, which can be any real number, so your solution would be:
( 2/3y-7/3 , y ) <---ordered pair
or
B) solve for y to get y=3/2x+7/2, but now x is your parameter, so your solution would be:
( x , 3/2x+7/2 ) <---------ordered pair
hope this helps explain

Answer 3

Put both equations in the "Slope-Intercept" form
y=mx+b
m is the slope
b is the y-intercept
If the slopes are different, the lines intersect at one point, i.e., one solution
If the slopes are the same, then you have to look at the y-intercept.
Same slopes, same intercepts the lines are the same line and have infinite solutions.
Sam slopes different intercepts, the lines are parallel and have no solutions

3x -2y = -7
Add -3x to both sides
-2y = -3x + -7
Multiply both sides by -1/2
y = (3/2)x + 7/2


-9x + 6y =21
Add 9x to both sides
6y = 9x+21
Multiply both sides by 1/6
y = (9/6)x + 21/6 Reduce the fractions
y = (3/2)x + 7/2

Now, review that stuff up at the top of this and make your determination: 0 solutions, 1 solution, or ifinite solutions?

Answer 4

This is going to turn out to be "no solution".

If you have 2 variables(or unknowns) as this problem does, then you need 2 equations. You have only 1 equation! Here's why.

Equation 1 is identical to equation 2. If I multiply equation 1 terms by -3, I get -9x +6y = 21 There's no way you can solve.

Here's another way to see the fact that these two equations are identical.

Eq. 1: 3x - 2y = -7
Eq. 2: -9x + 6y = 21

Multiply Eq. 1 by 3

9x - 6y = -21
-9x+6y = 21
Add ---------------------
0 + 0 = 0

Equations that are the same, even though they appear to be different, are called "linearly dependent"
Equations that aren't the same are, of course, called "linearly independent"

Good luck!

Answer 5

The second equation is -3 times the first one, so there are infinitely many solutions:

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

All solutions on the line defined by either equation (same line on both cases) are solutions.

Answer 6

First responder has a typo in one of the equations, making the rest of the work incorrect.

There is no solution. Both equations are actually the same thing, just not obvious. The second equations is equal to the first equation if you multiply the first by -3. You need two seperate and different equations to solve 2 variables.

Answer 7

You cannot eliminate one of the variables by addition or subtraction as you cannot solve for x or y. There are infinite solutions. Once you choose any value for y, you find x as follows.
x=(2y-7)/3

Answer 8

3x + 2y = 7 --------(1)
9x + 8y = 22 --------(2)
From (1): 2y = 7 - 3x
y = The coefficients of y in both equations will be numerically equal if we multiply (1) by 2 and (2) by 3, since the LCM of 6 and 4 is 12.

(1) x 2: 26x - 12y = 40 --------(3)
(2) x 3: 21x +12y = 54 --------(4)
(3) + (4): 47x = 94
x = 2

Substitute x = 2 into (1): 13(2) - 6y = 20
6 = 6y
y = 1

x = 2, y =1.

Answer 9

You can not solve this without knowing what either x or y is because you can only have 1 variable.

Answer 10

These are the same equations----no solution.