Slove. 2 + 6x = 1 - x and 5y + 4 = 4y + 5
AAAaannndd the bot gets it wrong yet again!
x=-3 does not work because
2+6(-3) = -15
1 - (-3) = 4
x = -1/7
7 x = -1 so x = -1/7
1 y = 1 so y = 1
To solve the equations 2 + 6x = 1 - x and 5y + 4 = 4y + 5, we will go through a step-by-step process for each equation.
1. 2 + 6x = 1 - x:
- Begin by combining like terms on each side of the equation.
- For the left side, there are no like terms, so it remains as 2 + 6x.
- For the right side, combine the 1 and -x to get 1 - x.
- Now the equation becomes 2 + 6x = 1 - x.
- Next, gather all the x terms on one side of the equation.
- To do this, add x to both sides of the equation.
- The equation now becomes 2 + 6x + x = 1 - x + x.
- Simplifying the equation gives 7x + 2 = 1.
- To isolate the x term, subtract 2 from both sides of the equation.
- This gives us 7x + 2 - 2 = 1 - 2.
- Simplifying further, we have 7x = -1.
- Finally, solve for x by dividing both sides of the equation by 7.
- The equation is now 7x/7 = -1/7.
- The solution is x = -1/7.
2. 5y + 4 = 4y + 5:
- Begin by combining like terms on each side of the equation.
- For the left side, there are no like terms, so it remains as 5y + 4.
- For the right side, combine the 4y and 5 to get 4y + 5.
- Now the equation becomes 5y + 4 = 4y + 5.
- Next, gather all the y terms on one side of the equation.
- To do this, subtract 4y from both sides of the equation.
- The equation now becomes 5y + 4 - 4y = 4y + 5 - 4y.
- Simplifying the equation gives y + 4 = 5.
- To isolate the y term, subtract 4 from both sides of the equation.
- This gives us y + 4 - 4 = 5 - 4.
- Simplifying further, we have y = 1.
- The solution is y = 1.
Therefore, the solution to the system of equations 2 + 6x = 1 - x and 5y + 4 = 4y + 5 is x = -1/7 and y = 1.