solve x+y=7
x-y=5 using elimination method
Just adding them they way they sit will eliminate the y
2x = 12
x=6
back in the 1st:
6+y=7
y = 1
x=6, y=1
Did not understood
Well, it seems like the equations are having a small disagreement. Let's see if we can help them patch things up using the elimination method!
To eliminate one variable, we can add the two equations together. So, if we add x+y=7 and x-y=5, we have:
(x+y) + (x-y) = 7 + 5
And when we simplify that, we get:
2x = 12
To solve for x, we divide both sides by 2, which gives us:
x = 6
Now that we have the value of x, we can substitute it into one of the original equations. Let's go with the first equation, x+y=7. Substituting x = 6 into that equation, we have:
6 + y = 7
Subtracting 6 from both sides gives us:
y = 1
So the solution to the system of equations x+y=7 and x-y=5 is x = 6 and y = 1. It seems like they've made up and found their common ground!
To solve the system of equations:
1) Start with the two equations:
x + y = 7
x - y = 5
2) Now we'll eliminate one of the variables by adding the two equations together. Add the left sides and the right sides separately:
(x + y) + (x - y) = 7 + 5
Simplifying the equation:
x + x + y - y = 12
2x = 12
3) Solve for x by dividing both sides of the equation by 2:
2x/2 = 12/2
x = 6
4) Now substitute the value of x back into one of the original equations. Choosing the first equation:
x + y = 7
6 + y = 7
5) Solve for y by subtracting 6 from both sides of the equation:
6 + y - 6 = 7 - 6
y = 1
6) The solution to the system of equations is x = 6 and y = 1.
To solve the system of equations using the elimination method, follow these steps:
Step 1: Write down both equations:
Equation 1: x + y = 7
Equation 2: x - y = 5
Step 2: Add the equations together vertically to eliminate one of the variables:
(x + y) + (x - y) = 7 + 5
Simplifying the equation, you get:
2x = 12
Step 3: Solve for x by dividing both sides of the equation by 2:
2x / 2 = 12 / 2
x = 6
Step 4: Substitute the value of x into either of the original equations to solve for y. Let's use Equation 1:
6 + y = 7
Subtract 6 from both sides of the equation:
y = 7 - 6
y = 1
Step 5: Check the solution by substituting the values of x and y back into both original equations:
For Equation 1: 6 + 1 = 7 (True)
For Equation 2: 6 - 1 = 5 (True)
Therefore, the solution to the system of equations is x = 6 and y = 1.