Without graphing, name the ordered pair where the graphs of the two linear equations intersect.
(Below is the system.)
{ x = 2
y = -3
Without graphing, name the ordered pair where the graphs of the two linear equationd intersect.
(Below is the system.)
{ y = 2
x + 2y = 10
For this second problem, I found that the x and y intercepts for x + 2y = 10 should be -1 and 5, respectively. However, I'm stumped on both problems as to how I'm supposed to handle the linear equations like "y = 2." If I could have some assistance with that, that would be great! :)
these are just vertical or horizontal lines.
clearly, the first set of equations intersect at (2,-3)
The second intersect where y=2
so, plugging that into the second equation,
x+2*2=10
x = 6
and they intersect at (6,2)
Having said that, and solved the systems, go ahead and graph the lines to get more of a feel for how they work.
hey steve its been a while
To find the ordered pair where the graphs of the two linear equations intersect, we can substitute one equation into the other and solve for the variables. Let's work on each problem separately:
1. { x = 2
y = -3
Since x is already given as 2, we can substitute this value into the second equation:
y = -3
Therefore, the ordered pair where the graphs of these equations intersect is (2, -3).
2. { y = 2
x + 2y = 10
In this case, we can substitute the value of y (which is 2) into the second equation:
x + 2(2) = 10
Simplifying the equation:
x + 4 = 10
x = 10 - 4
x = 6
Therefore, the ordered pair where the graphs of these equations intersect is (6, 2).
To find the ordered pair where the graphs of the two linear equations intersect, we need to solve the system of equations simultaneously. Let's start by solving the first system:
{ x = 2
y = -3
In the first equation, we already have x = 2. Substituting this value into the second equation, we get:
y = -3
So, the ordered pair where the graphs intersect in the first system is (2, -3).
Now let's move on to the second system:
{ y = 2
x + 2y = 10
In the first equation, we have y = 2. Substituting this value into the second equation:
x + 2(2) = 10
Simplifying:
x + 4 = 10
Subtracting 4 from both sides:
x = 6
So, the x-coordinate of the ordered pair is 6. Plugging this value back into the first equation, we get:
y = 2
The y-coordinate of the ordered pair is 2.
Therefore, the ordered pair where the graphs intersect in the second system is (6, 2).
To summarize:
- In the first system, the ordered pair is (2, -3).
- In the second system, the ordered pair is (6, 2).