Estimate the intersection point of the graphs of the following linear equations in two variables.
y=x+2
y=−x+6
To find the intersection point of the two linear equations, we can set them equal to each other:
x + 2 = -x + 6
Combining like terms, we get:
2x = 4
Dividing both sides by 2, we find:
x = 2
Now, we substitute this value back into one of the equations to find the corresponding y-value:
y = 2 + 2
y = 4
Therefore, the intersection point of the two graphs is (2, 4).
To find the intersection point of the two linear equations, we need to set their y-values equal to each other and solve for x.
Given equations:
1) y = x + 2
2) y = -x + 6
Setting the y-values equal to each other:
x + 2 = -x + 6
Combining like terms:
2x = 4
Dividing both sides by 2:
x = 2
Now, substitute the value of x into either equation to find the y-value:
Using equation 1:
y = 2 + 2
y = 4
Therefore, the intersection point of the two graphs is (2, 4).
To estimate the intersection point of the graphs of the given linear equations y = x + 2 and y = −x + 6, we need to find the values of x and y that satisfy both equations simultaneously.
We can do this by solving the system of equations.
Step 1: Set the two equations equal to each other:
x + 2 = -x + 6
Step 2: Combine like terms:
2x = 4
Step 3: Divide both sides by 2 to solve for x:
x = 2
Step 4: Substitute the value of x back into either equation to find y. Let's substitute it into the first equation:
y = 2 + 2
y = 4
So, the estimated intersection point of the graphs is (2, 4).