+2448 
Need help asap, Could you maybe answer the first couple and I try the next ones? Then correct me if i'm wrong because i really want to understand this.
+4622 (1) We have 3x+y=-2, 2x-3y=-5. We want to find a value of x that equals y. So, bringing 3x to the other side in the first equation, we get: y=-2-3x. The second equation: 2x-3y=-5, -3y=-5+2x, y=-5+2x/-3.
So, -2-3x=-5+2x/-3, so x=-11/7. Plugging the value of x in, in order to solve for y, we get: 3(-11/7)+y=-2, y=19/7.
+130071 Yep. after some manipulation as Tertre has done...... each problem wil have a variable already defined in one of the equations...just substitute the value for that variable into the other equation ....you will then have a variable in one equation that is easy to solve
BTW...thanks Tertre !!!!
+130071 Try 6......post your answer....even if it's incorrect....we can still fix that !!!
+2448 Oh shoot I started on 7 but ill do 6 as well hold on might take a bit
+2448 Okay so first....Am I even starting this off right. My head really hurts rn >.< like literally.
x+4y=-6-->4y=-6x
8x-2y=-14-->-2y=-14+8x
+2448 Okay um -2y=-14+8x divide by -2 on both sides so y=-14+8x/-2
4y=-6x divide by 4 on both sides as well and you get y=-6x/4
-6x/4=-14+8x/-2
So far so good? or am i totally wrong?
+130071 You're not wrong...but the there is an easier way without resorting to those nasty fractions
6)
x + 4y = --6
8x - 2y = -14
Do you see that we have a single variable in the first equation ???...in this case, x
So subtract 4y from both sides and we get x = -6 - 4y
Now..in the second equatiion....just substitute this for x and we have
8 [ -6 - 4y ] - 2y = -14 simplify
-48 - 32y - 2y = -14
-48 - 34y = -14 add 48 to both sides
-34y = 34 divide both sides by -34
y = -1
The beauty here is that we already have an expression for x...we just need to fill in the y value
x = -6 - 4(-1) = -6 + 4 = -2
So (x, y) = ( -2, -1)
As a hint on number 7...note that 7x + y = 7 can be transformed into y = 7 - 7x
Can you take it from here???...post your work if you get stuck...I'll see if I can "un-stick" you !!...LOL!!!!
+2448 Oh wait I can try 7! 7x+y=7 ( subtract 7x from both sides)
y=7-7x
4x+3(7-7x)=21
(21-21x)
4x+21-21x=21
25x+21=21
-21 -21
25x do I divide it by 25 to get 1?
x=1
y=7-7(1)
y=7-7
y=0
(x,y)-->(1,0)
+130071 Good try !!!... you have the right idea..just a small error
Let's take it from here....
4x+3(7-7x)=21
4x + 21 - 21x = 21 subtract 21 from both sides
4x - 21x =0
-17x = 0 ⇒ x = 0
Sub this back into y = 7 - 7x → y = 7 - 7 (0) = 7 - 0 = 7
(x,y) =(0,7) ...check this solution in both equations to see that this is true....!!!!
+2448 I knew I wouldn't have gotten it correct -_-
I tried 8 but it's obviously completely wrong. *sigh*
x+7y=23
-7y -7y
x=23-7y
8(23-7y)-3y=7
184-56y-3y=7
and here is where it all goes wrong...
184-53y=7
-184 -184
53y=-177
/53 /53
y=-3.34 or something like that >.<
and i'll wait to see if i'm even correct first
+130071 184-56y-3y=7
and here is where it all goes wrong...
LOL!!!!!.....Just a math error....
184 - 59y = 7 subtract 184 from both sids
-59y = -177 divide both sides by -59
y = 3
Sub this back into x=23-7y to find x...and you're finished !!!
You made a really good try...!!!
+2448 x= 2
y=3
(2,3)
Thanks I have 2 more that are a bit different cuz they involve 3 each and also a,b, and c. Would you be able to help with that seperately?
+130071 If you're still onboard...let me show you how to solve these with something known as Cramer's Rule
Here's 6...which we know the answer to
x + 4y = -6
8x - 2y = -14 we have the equations lined up properly....
Now write the left side just using the coefficients
1 4
8 -2 [ multiply (1 * -2) diagonally = -2 ..... subtract the product of the other diagonal = ( 8 * 4) = 32 ]
So we have -2 -(32) = -34 (1) [as long as this isn't 0, we're Ok]
Sub the -6 and -14 into the 1st column of (1) ...this will be the "x" column"
-6 4
-14 -2 [ repeat the process we just did... (-6 * -2) - ( 4 * -14) = ( 12 - (-56) ) = 68
Divide this result by the result from (1) and we get 68 / -34 = -2 = x
Now sub -6 and -14 into the second column of (1)...this will be the "y" column ... and repeat the process
1 -6
8 -14 (1 * -14) - ( -6 * 8) = ( -14 ) - ( -48) = -14 + 48 = 34
Divide this result by (1) to get y = 34/ -34 = -1
So (x, y) = ( -2, -1) ....exactly what we had before !!!
