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Question

5X-2Y=-9
7X+3Y=-1

Answer 1

get at least the x or y to be the same number with opposite signs

multiply the first row by 3 and the second by 2
3 (5x-2y=-9)
2 (7x+3y=-1)

15x-6y=-27
14x+6y=-2

add the common terms

29x + 0y = -29
29x = -29

divide

x=-1

Answer 2

I suppose this is a system that you need to solve? Here's how you do it. Since they're both in standard form, it would be easiest to solve by linear combination aka the addition method. Eliminate the Y becuase the y coeffieients, that is, numbers in front of the y are smaller, and therefore easier, than the numbers in front of the x. Since all your coefficients are relatively prime yo'll have to multiply both equations by constants, and multpilying smaller numbers is less likely to introduce mistakes than multiplying larger numbers. Here goes ...

3(5X - 2Y = -9)
2(7X + 3Y = -1)

This gives you...
15X - 6Y = -27
14X + 6Y = -2
--------------------
29X + 0Y = -29
x = -1
Now plug x = -1 into either equation to find y: Again, I like to use the one with the smaller coeffieicnts.
5(-1) - 2y = -9
-5 - 2y = -9 add 5 to each side to isolate the -2y on the left:
-2y = -4, y = 2
Finally, put both numbers into the equation that you didn't use to find y, and make sure they both work
7(-1) + 3(2) = -7 + 6 = -1

You could also use the substitution method, and get the same result, but it's easier to use that method when you already have one of the variables isolated (by itself). You want to learn both methods, since sometimes one method is easier than the other, and easier means better understanding and fewer mistakes. Also sometimes your test or your teacher may require you to use one method or the other. Other ways of solving are matrices, and graphing. Tho your solution by graphing is only as good as your graph.

Answer 3

ok...


1) 5x-2y = -9
2) 5x = 2y - 9
3) x = (2y - 9)/5

substitute into second equation:

4) 7x+3Y = -1
5) (7(2y - 9)/5) +3y = -1
6) ((14y - 63)/5) + 3y = -1 (multiply all terms by 5 to get:)
7) 14y-63 + 15y = -5
8) 14y + 15y = 58
9) 29y = 58
10) Therefore y = 2

So substitute y = 2 back into first equation to get x.

11) 5x - 4 = -9
12) 5x = -5

Therefore x = -1

I put way more steps in there than I usually would just in cae.

Answer 4

Depends what grade you're in. If you can use matrices, use Gauss-Jordan elimination, or if not, isolate one variable:
5x = -9 + 2y
x = (-9 + 2y)/5

Plug it into the next equation:
7(-9 + 2y)/5 + 3y = -1
-63 + 14y + 15y = -5
29y = 58
y = 2

x = (-9 + 2y)/5
x = -1

Yay, all done!

Answer 5

Multiply top equation by 3 and bottom equation by 2 to get:
15x-6y=-27
14x+6y=-2

Add the equations:
29x=-29
x=-1

Plug x=-1 into one of the original equations.
5(-1)-2y=-9
-5-2y=-9
-2y=-4
y=2

Therefore:
x=-1
y=2

Answer 6

5X - 2Y = -9 -------------------------(1)
7X + 3Y = -1-------------------------(2)

from (1)

2Y = 9 + 5X
Y = 4.5 + 2.5X

replace Y in (2)

7X + 3(4.5 + 2.5X) = -1

14.5 X = -1 - 13.5
14.5 X = -14.5
X = -1
Y = 4.5 + 2.5(-1)
= 2