X-5y=7 and 3x-2y=-4 find the solution to both equations the intersection point is

Answer 1

To find the intersection point of these two equations, we can solve the system of equations by either substitution or elimination method.

Using the elimination method:

Multiply the first equation by 3 and the second equation by 5 to eliminate the x term:
3*(X-5y) = 3*7
5*(3x-2y) = 5*(-4)

This simplifies to:
3X - 15y = 21
15x - 10y = -20

Now, add the equations together to eliminate the y term:
(3X - 15y) + (15x - 10y) = 21 + (-20)
3X + 15x - 15y - 10y = 1
18x - 25y = 1

Now we have the following equation:
18x - 25y = 1

To solve for x, we can multiply the second equation by 18/3 = 6 and subtract it from the multiplied first equation:
6*(X-5y) = 6*7
18x - 12y = -24

This simplifies to:
18x - 30y = 42

(18x - 25y) - (18x - 30y) = 1 - (-24)
-25y + 30y = 1 + 24
5y = 25
y = 5

Substitute the value of y = 5 into one of the original equations:
X - 5*5 = 7
X - 25 = 7
X = 7 + 25
X = 32

So, the solution to both equations is X = 32 and y = 5.