Question

Please Help!

Solve the following system of equations and show all of your work.

4x + 3y = -1
3x + y = 3

Answer 1

What methods have you worked on?
For example, substitution, elimination, Cramer's Rule, comparison.

Answer 2

elimination because its easier

Answer 3

I got
4x + 3y = -1
3x + y = 3

x + 2y = 2
2y/2 = 2/2
y=1 but i dont know how to solve for x please help

Answer 4

To solve by elimination, you need to multiply one or both equation by numbers so that the coefficient of one of the variables match. Add or subtract to eliminate the variable and subsequently solve for one of them.
What you have done is to reduce the coefficient of x to 1, but not ELIMINATE.
You are almost there.
4x + 3y = -1 ...(1)
3x + y = 3 ...(2)

Multiply (2) by 3 and subtract (1), that gives you 3y-3y=0y so y is eliminated.
The solve the remainder of the equation for x.

To find y, use the value of x to substitute into equation (2) and solve for y.

Answer 5

I kinda get it but can you show me the steps because i don't understand what you wrote?

Answer 6

y = -4?

Answer 7

4x + 3y = -1 ...(1)
3x + y = 3 ...(2)

Multiply (2) by 3 and subtract (1)
9x + 3y = 9 ...(2a)
4x + 3y = -1 ...(1)
subtract to get:
5x + 0y = 10 (3)
Solve for x to get
x=10/5=2 (4)

Substitute (4) into (2)
3(5) + y = 3 ....(2)
Can you solve for y now?

Answer 8

4x + 3y = -1 ...(1) <------why do you put (2) ?
3x + y = 3 ...(2) <----(1)?

Answer 9

The original equations are defined as:
4x + 3y = -1 ...(1)
3x + y = 3 ...(2)

When we found the value of x in equation (4):
x=10/5=2 (4)
we have a choice of substituting x into equation (1) or (2).

Answer 10

I have chosen to substitute (4) in (2) because the coefficient of y in (2) is 1, so there is less work:
3(2)+y=3 ....(2b) [ note, I have made a correction, since x=2 (not 5) in my previous solution]
which makes
6+y=3 that solves to
y=3-6=-3

Answer 11

Now the only thing left to do is to substitute x=2 and y=-3 into the original equations (1) and (2) to verify that the solution is indeed correct.

Answer 12

ohh ok
but i did this
3 (4x + 3y = -1 )
-4 (3x + y = 3)

12x + 9y = -3
-12x - 4y = -12
5y = -15
y = -3

Answer 13

is that correct?

Answer 14

i get it now you have been a really great help(: thank you soo much!(:

Answer 15

Yes, that's correct!
You could eliminate either one.
Eliminating x first gives you good practice!