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Question

I need help with these Math Equations..
Please help solve them... with the work THANK YOU!! = ]

1) y = -x +3
y= x +1


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



3)y=1/2x + 3
x + 4y =24



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



5)y= -x -2
2x -3y = -9



6)y=2x-1
y=x + 1



7) y= 2/3x + 1
x = 6

Answer 1

y = - x + 3- - - - - -Equation 1
y = x + 1- - - - - - -Equation 2
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convert equation 1 to standard

y = - x + 3

x + y = - x + 3 + x

x + y = 3. . . . .Standard form

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Insert equation y value into standard form equation 1

x + y = 3

x + x + 1 = 3

2x + 1 = 3

2x + 1 - 1 = 3 - 1

2x = 2

2x / 2 = 2/ 2

x = 2/2

x = 1

Insert the x value into equation 1

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y = - x + 3

y = - 1 + 3

y = 2

Insert the y value into equation 1

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Check for equation 1

y = - x + 3

2 = - 1 + 3

2 = 2

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Check for equation 2

y = x + 1

2 = 1 + 1

2 = 2

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Both equations balance

The solution set { 1, 2 }

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Answer 2

1) -x +3 = x + 1 since both = y Add x and subtract 1 to get
2 = 2x So x = 1 and y = 1 + 1 or 2

2) 2x - 4 = -1/2x + 1 Simplify by mult by 2 to : 4x -8 = -x + 2
5x = 10 so x = 2 and y = 4 - 4 or 0

3) Substitute the value of Y into second equation, to get : x + 4(1/2x + 3) = 24 Clear to get x + 2x + 12 = 24 Now you can solve it from here to get X, Use x value in either equation to find y

4) Make first equation y = 3 - x (Subtract x from both sides). Then -2x + 3 - x = -6 : Combine like terms (add x, subtract 3) and solve for x. I will tell you that y = 0. Watch your signs!

5) 2x -3(-x -2) = -9 by substitution. When you cleared parenthesis, did you get a +3x or -3x ?
It's 3x, since negative times negative is positive and +6 for the same reason. So it's 5x + 6 = -9 and later, -(-3) - 2 to find the value for y.

6) 2x - 1 = x + 1 Solve like 1) by subtracting x and adding 1
to get x directly. Plug x value into 2nd equation to get y value.

7) You know x, so solve y by making first equation y = 6(2/3) + 1 .

Answer 3

They are all done similarly. Here's the first:

y = -x +3
y = x +1

Therefore, x + 1 = -x + 3
x = -x + 3 - 1
x = -x + 2
x + x = 2
2x = 2
x = 1

If x = 1 and y = x + 1
Then y = 1 + 1
y = 2

Does that help you solve the rest?

Answer 4

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

2)y=2x -4
y=-1/2x + 1
4y= -2x + 4
5y=0
y=0
x=2

3)y=1/2x + 3
4y=2x + 12
2x - 4y = -12
x + 4y =24
3x=12
x=4
y=5

4)x+y=3
-2x + y = -6
2x -y =6
3x=9
x=3
y=0

5)y= -x -2
x + y =-2
-2x-2y= 4
2x -3y = -9
-5y=-5
y=1
x=-3

6)y=2x-1
y=x + 1
0=x -2
x=2
y=3

7) y= 2/3x + 1
x = 6

y=2/3 *6 + 1=4+1=5
x=6

Answer 5

1) y = -x +3
y= x +1

y=y
-x +3=x+1
2=2x

x=1
y=2