Review the graph of a system of two linear equations in two variables X minus 5Y equals seven and 3X minus 2Y equals -4. Find a solution to both equations what is the intersection point

Answer 1

To review the graph of the system of equations, let's start by solving the system.

Given the system of equations:
1) X - 5Y = 7
2) 3X - 2Y = -4

To find the solution to both equations (the intersection point), we can use any method of solving systems of equations, such as substitution or elimination. In this case, let's use the method of elimination.

Multiply equation 1 by 3 and equation 2 by 5 to make the coefficients of X cancel each other when the equations are added together:

3(X - 5Y) = 3(7) -> 3X - 15Y = 21
5(3X - 2Y) = 5(-4) -> 15X - 10Y = -20

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

Now, we have a new equation:
3X - 2Y = -4 -> 18X - 12Y = -24

Next, we can solve the new equation for X:
18X - 25Y = 1 -> 18X = 1 + 25Y -> X = (1 + 25Y)/18

Substitute this value of X back into equation 1:
X - 5Y = 7 -> ((1 + 25Y)/18) - 5Y = 7

Multiply through by 18 to eliminate the fraction:
1 + 25Y - 90Y = 126 -> -65Y = 125

Solve for Y:
Y = 125/(-65) -> Y = -25/13

Substitute this value of Y back into the expression for X:
X = (1 + 25Y)/18 -> X = (1 + 25(-25)/13)/18 -> X = 26/13

Therefore, the solution to both equations (the intersection point) is (X, Y) = (26/13, -25/13).