Answer: The equations are y = 4x-3 and y= 3x -1
Explanation:
So lets say both equations will have positive slopes. Using that, we can input any slope and solve for the y intercept using the coordinates.We will use the formula, y=mx + b where m is the slope and b is the y-intercept
Let's say the slope is 3.
5 = 3(2) + b
5= 6 + b
-6 -6
b= -1
We can now come up with the equation, y= 3x -1
We need to find another equation that will intersect with it at the point (2,5)
For lines to intersect, they need to have different slopes and different y-intercepts.
We need to come up with a new slope, the slope of the second equation could be 4. Now using the formula, use the coordinates so solve for the y intercept.
5= 4(2) + b
5 = 8 + b
-8 -8
b = -3
The equation will be y = 4x -3
We now have the equations y=4x -3 and y = 3x -1
To find that their solution is (2,5) substitute one of the y-values into the other and solve for x then solve for y.
4x -3 = 3x -1
+3 +3
4x = 3x + +2
-3x -3x
1x = 2
x = 2
We know now that the value of x is true because the value of x is 2.Input it into one of the equations and solve for y.
y = 4(2) - 3
y = 8-3
y = 5
The solution is indeed (2,5) .