A system of equations is shown below:
x + y = 3
2x − y = 6
The x-coordinate of the solution to this system of equations is _____.
I'm thinking it could be X=3
Your thinking could be right, but what made you think it is, and why ?
A system of equations is shown below:
6x − 5y = 5
3x + 5y = 4
The x−coordinate of the solution to this system of equations is _____.
To solve this equations, you have to use the elimination or addition method. You have to eliminate the y's since you want to find the x-coordinate. Then solve for the rest of the equation...
To find the x-coordinate of the solution to the system of equations, we can solve the system of equations using one of the common methods such as substitution or elimination. Let's use the substitution method:
1. Start with the given system of equations:
x + y = 3 ---(1)
2x - y = 6 ---(2)
2. Solve equation (1) for x in terms of y:
x = 3 - y
3. Substitute the value of x in equation (2):
2(3 - y) - y = 6
4. Simplify and solve for y:
6 - 2y - y = 6
6 - 3y = 6
-3y = 0
y = 0
5. Substitute the value of y back into equation (1) to find x:
x + 0 = 3
x = 3
Therefore, the x-coordinate of the solution to the system of equations is x = 3.
So, your initial thought is correct. The answer is x = 3.