This is a substitution equation. Would that change the steps that you did?
Y=3x+1
Y=5x-3
Answer says x=-2 and y=7
Please explain steps. Thanks
math help - MathMate, Monday, April 23, 2012 at 10:25pm
Y=3x+1 ...(1)
Y=5x-3 ...(2)
By comparison of (1) and (2), we conclude that
3x+1=Y=5x-3
3x+1=5x-3
solve for x to get
2x=4
x=2
Put x=2 in (1) to get
Y=3(2)+1=7
Check:
put x=2 in (2) to get
Y=5*2-3=7
If your program gives x=-2 and y=7, there must be a typo somewhere. Check your post
y = 3 x + 1
y - 1 = 3 x Divide both sides by 3
( y - 1 ) / 3 = x
x = ( y - 1 ) / 3
y = 5 x - 3
y = 5 * ( y - 1 ) / 3 - 3
y = ( 5 / 3 ) * ( y - 1 ) - 3
y = 5 y / 3 - 5 / 3 - 3
y = 5 y / 3 - 5 / 3 - 9 / 3
y = 5 y / 3 - 14 / 3
y - 5 y / 3 = - 14 / 3
3 y / 3 - 5 y / 3 = - 14 / 3
- 2 / 3 y = - 14 / 3 Multiply both sides by - 3
2 y = 14 Divide both sides by 2
y = 14 / 2
y = 7
x = ( y - 1 ) / 3
x = ( 7 - 1 ) / 3
x = 6 / 3
x = 2
x = 2 , y = 7
Or very simply :
y = 3 x + 1
y = 5 x - 3
3 x + 1 = 5 x - 3
3 x - 5 x = - 3 - 1
- 2 x = - 4 Divide both sides by - 2
- 2 x / - 2 = - 4 / - 2
x = 2
y = 3 x + 1
y = 3 * 2 + 1 = 6 + 1 = 7
y = 5 x - 3
y = 5 * 2 - 3 = 10 - 3 = 7
x = 2 , y = 7
To solve the system of equations, we can follow these steps:
1. Write down the given equations:
Y = 3x + 1
Y = 5x - 3
2. Since both equations are equal to Y, we can set them equal to each other:
3x + 1 = 5x - 3
3. Next, we want to solve for x. To do that, we can begin by isolating the x terms on one side of the equation:
3x - 5x = -3 - 1
-2x = -4
4. Now, we can solve for x by dividing both sides of the equation by -2:
x = -4 / -2
x = 2
5. We have found the value of x. To find the value of Y, we can substitute x = 2 into either of the original equations. Let's use the first equation, Y = 3x + 1:
Y = 3(2) + 1
Y = 6 + 1
Y = 7
Thus, the solution to the system of equations is x = 2 and Y = 7.
Note: The given answer you mentioned, x = -2 and Y = 7, is inconsistent with the original equations. Therefore, there may have been an error in the calculation or in the problem itself.