Question

Help fast? I have 2 questions! ***I FAN AND MEDALLL***

1.Solve the system of equations.

5x + y = 9
3x + 2y = 4

A) (-2, 5)
B) (1, 4)
C) (2, -1)
D) (4, -4)

2.
Choose the equivalent system of linear equations that will produce the same solution as the one given below.

6x + 2y = -6
3x - 4y = -18


A) 12x + 4y = -12
15x = -30

B) 8x + 4y = -4
14x = -10

C) 6x - 8y = -36
-6y = -42

D) 6x - y = -15
3y = 9

Answer 1

1. Choose the first variable you want to solve for and then substitute for the other equation. I will chose to solve for y with the first equation and then use substitution for the second:
5x+y=9
y=9-5x
Now use this instead of y for the second equation:
3x + 2(9-5x) = 4
3x + 18 - 10x = 4
Now combine like terms by moving the variables to one side and the numbers to the other:
18-4=10x-3x
14=7x
x=2
Now that you now the value of x, revisit the first equation to find y by using substitution:
5x+y=9
y=9-5x
y=9-5(2)
y=9-10
y=-1
So, the final answer to question 1 is C. , (2,-1)

Answer 2

2. As for question 2, you also need to solve the given system of equations first, before finding one with the same solution.

Answer 3

I have one more problem that I'm not sure about, can you help me with it?

Answer 4

Sure :) I have to leave soon but one more is fine :D

Answer 5

Glad to help! @dancingdiamond :)

Answer 6

Thanks!:
Solve the system of equations by substitution. What is the solution for x?

2x + y = 1
4x + 2y = -1

A) x = 0
B) x = 2
C) There is no x value, as there is no solution.
D) x can be any value, as there is an infinite number of solutions.

What should I do first in this? I know what the subsitutuion method is but I'm not sure exactly how to solve the system for X

Answer 7

To solve for x you first have to pay attention to the other variable,y, that way when you are substituting, you are only using the variable x, and vice versa (if you start by looking towards x, substitution will end up having you use only y and that will cause you to do extra work). So look at y:
2x+y=1
y=1-2x
Now use 1-2x instead of y for the second equation to solve for x:
4x+2y= -1
4x+2(1-2x)= -1
4x+2-4x = -1
Now combine like terms:
4x-4x=-1 - 2
4x-4x=-3
^ 4x - 4x is 0 or 0x, and 0 is not equal to-3, nor does it make sense (there is no x variable anymore), so there is no solution. The final answer is C., because there is no solution for x.

Answer 8

An explanation for this is that if 0= -3, then that means that the linear equations of the system are different, so they are parallel, as there is NEVER a point of intersection between the two lines. If there was a point of intersection, there would be a solution, so no solution here. @dancingdiamond

Answer 9

...Well happy studying! :) Happy to help, message me or tag me if you have anymore questions and I will try to respond as soon as possible.

Answer 10

Thank you so much!!

Answer 11

Np! :)