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

the intersection point is

1 answer

To find the solution to both equations, we can use the method of substitution or elimination. Let's use the method of elimination.

We start by multiplying the first equation by 3 and the second equation by -5 to make the coefficients of x in both equations the same:

3(x-5y) = 3(7) => 3x - 15y = 21
-5(3x-2y) = -5(-4) => -15x + 10y = 20

Now, we can add the two equations together to eliminate the x term:

(3x - 15y) + (-15x + 10y) = 21 + 20
-12y = 41

Solving for y, we divide both sides of the equation by -12:

y = (-41) / (-12) = 41/12

Now that we have the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:

x - 5(41/12) = 7
x - 205/12 = 7
x = 7 + 205/12
x = 84/12 + 205/12
x = 289/12

Therefore, the solution to both equations is (x, y) = (289/12, 41/12).