Where do the graphs of the following equations intersect.
X+y=4 and x-y=2 is this one x=2+y (0,-2)
Also write two equations whose graphs intersect at the origin (0,0)
You must solve the 2 equations to find their intersection.
just add them the way they sit:
x+y = 4
x-y = 2
...........
2x = 6
x = 3
sub that back into either one: ----> y = 1
so they intersect at (3,1)
for your 2nd , any straight line going through the origin can't have a y-intercept, so ,,,
To find the intersection points of the graphs of the given equations, we can solve them simultaneously. Let's start with the equations:
1) X + y = 4
2) x - y = 2
To solve these equations, we can use the method of substitution or elimination:
Method 1 - Substitution:
Let's solve equation 2) for x:
x = 2 + y
Substitute this value of x into equation 1):
(2 + y) + y = 4
2y + 2 = 4
2y = 2
y = 1
Substitute this value of y back into the equation for x):
x = 2 + 1
x = 3
So the solution is (x, y) = (3, 1).
Method 2 - Elimination:
Add the two equations together:
(X + y) + (x - y) = 4 + 2
X + x = 6
2x = 6
x = 3
Substitute this value of x into either of the original equations (let's use equation 1)):
3 + y = 4
y = 1
So the solution is (x, y) = (3, 1).
Now, for the second part of your question, let's find two equations whose graphs intersect at the origin (0,0). One way to achieve this is by setting both the x and y intercepts of the equations to be zero.
Equation 1: x = 0
The graph of this equation is a vertical line passing through x = 0 (the y-axis). It intersects the origin (0,0).
Equation 2: y = 0
The graph of this equation is a horizontal line passing through y = 0 (the x-axis). It also intersects the origin (0,0).
So the two equations whose graphs intersect at the origin are x = 0 and y = 0.