There are two ways to solve that: elimination and substiution. In elimination, you would sort of stack the equations on top of eachother, and add or subtract them. In your case, it would look like this.
X + 5y = -7
-2x -3y = 7
your goal is to eliminate one variable. In this case, x is very easy to eliminate. You have x on top and -2x on bottom, and your goal is to get to 0x. You can multiply the entire first equation like this 2(x + 5y = -7). Now you have 2x + 10y = -14. Looking like this
2x +10y = -14
+
-2x -3y =7
we are adding the equation because 2 + (-2) gives you 0, eliminating the variable x from the equation. If both 2xs were positive, then we would subtract the equations. After adding the eqations verticly, we get
0x +7y = -7. or 7y = -7
to solve for y now, you divide both sides of the equation by the coefficient (the number in front of the variable, y). You are now left with y = -1.
With that number, you get to pick either of the two ORIGINAL equations (either x + 5y = -7 or -2x - 3y = 7 and plug the number -1 in for y. The first one looks easier, so I will use that. X + 5(-1) = -7 or x - 5 = -7. to get x alone, subtract 5 from both sides to get x = -2.
The answer to that equation is x = -2, y = 1.
Edit: done using an iPod touch, missed a negative sign, screwed it all up, but fixed it.
Answers & Comments
Verified answer
[x + 5y = -7]3 multilpy equation by 3
[-2x - 3y = 7]5 multiply equation by 5
-----------------------
...3x+15y=-21
-10x-15y=35
---------------------
-7x=14
x=-2 answer//
plug in -2 to x+5y=-7
-2+5y=-7
5y=-7+2
5y=-5
y=-1 answer//
solution set is (-2,-1) answer//
There are two ways to solve that: elimination and substiution. In elimination, you would sort of stack the equations on top of eachother, and add or subtract them. In your case, it would look like this.
X + 5y = -7
-2x -3y = 7
your goal is to eliminate one variable. In this case, x is very easy to eliminate. You have x on top and -2x on bottom, and your goal is to get to 0x. You can multiply the entire first equation like this 2(x + 5y = -7). Now you have 2x + 10y = -14. Looking like this
2x +10y = -14
+
-2x -3y =7
we are adding the equation because 2 + (-2) gives you 0, eliminating the variable x from the equation. If both 2xs were positive, then we would subtract the equations. After adding the eqations verticly, we get
0x +7y = -7. or 7y = -7
to solve for y now, you divide both sides of the equation by the coefficient (the number in front of the variable, y). You are now left with y = -1.
With that number, you get to pick either of the two ORIGINAL equations (either x + 5y = -7 or -2x - 3y = 7 and plug the number -1 in for y. The first one looks easier, so I will use that. X + 5(-1) = -7 or x - 5 = -7. to get x alone, subtract 5 from both sides to get x = -2.
The answer to that equation is x = -2, y = 1.
Edit: done using an iPod touch, missed a negative sign, screwed it all up, but fixed it.
x + 5y = –7
–2x – 3y = 7
Since there's nothing to be cancelled, a certain value must be distributed. Here, I'll use 2.
2(x + 5y = –7)
–2x – 3y = 7
2x + 10y = -14
-2x - 3y = 7
Cancel 2x and -2x, since they sum up to 0.
10y = -14
-3y = 7
Add.
7y = -7 (Divide both sides by 7)
y = -1
Getting x:
x + 5(-1) = –7
x - 5 = - 7
x = - 7 + 5
x = - 2
Checking:
x + 5y = –7
-2 + 5(-1) = -7
-2 - 5 = - 7 (True)
–2x – 3y = 7
–2(-2) – 3(-1) = 7
4 + 3 = 7 (True)
Thus, x = -2, and y = -1.
Solution Set: (-2, -1)
Hope this helps.
I assume the parenthesis is just for presentation purposes and not part of the equation.
x+5y=-7 (Equation 1)
-2x-3y=7 (Equation 2)
Equation 1 can be rearranged to become:
x=-7-5y (Equation 3)
Substitute x of Equation 2 with Equation 3:
-2(-7-5y)-3y=7
14+10y-3y=7
7y=-7
y=-1
Substitute y of Equation 3 with -1:
x=-7-5(-1)
x=-7+5
x=-2
Answer x=-2, y=-1
x=-2, y=-1
0
x + 5y = -7
x = -7 -5y
-2x -3y = 7
-2(-7 -5y) -3y = 7
14 +10y -3y = 7
14 +7y = 7
7y = 7-14 = -7
y = -1
x +5(-1) = -7
x -5 = -7
x = -7+5 = -2
The answer is x=-2, y=-1
In coordinate system form its (-2,-1)
y=-1, x=-2
(x= 5y -7) x= -12y
12y/12=1
X=X
(-2x- 3y = 7)
-3y=7-2x
-3y=5x
-3y/-3 = 5x/-3
y= 1 2/5 x
y=7?
(0,7)
haha, I dont know! :)
y= -3 & x= 8