Graph two lines to find x and y values that make both y=−23x+3 and y=2x−5 true.
To find the values of x and y that make both equations true, let's graph the two lines and see where they intersect. The coordinates of the intersection point will give us the values of x and y.
We'll start by graphing the first equation, y = -23x + 3. To do this, we need to create a table of values for x and y.
Let's choose a few values for x and calculate the corresponding y values.
For example, let's start with x = -2:
y = -23(-2) + 3
y = 46 + 3
y = 49
Now let's choose x = 0:
y = -23(0) + 3
y = 0 + 3
y = 3
Finally, let's choose x = 2:
y = -23(2) + 3
y = -46 + 3
y = -43
Now we can plot these points on a graph and connect them with a line.
Next, let's graph the second equation, y = 2x - 5. Again, we'll create a table of values for x and y.
For x = -2:
y = 2(-2) - 5
y = -4 - 5
y = -9
For x = 0:
y = 2(0) - 5
y = 0 - 5
y = -5
For x = 2:
y = 2(2) - 5
y = 4 - 5
y = -1
We'll plot these points on the same graph as the first equation, and connect them with a line.
Now, we can visually see where the two lines intersect. The coordinates of this intersection point will give us the values of x and y that make both equations true.
By looking at the graph, it appears that the intersection point is approximately (2, -1). So the values of x and y that satisfy both equations are x = 2 and y = -1.
well, if both right hand sides equal y then they are equal so
-23 x + 3 = 2 x - 5
-25 x = -8
x = 8/25
then
use either
y =2 x - 5
y = 16/25 - 125/25 = -109/25