review the graphs of a system of two linear equations in two variables: x - 5y + 7 and 3x - 2y = -4. find the solution to both equations. The Intersection point is()
To review the graphs of the system of two linear equations, let's first write them in slope-intercept form (y = mx + b) where m is the slope and b is the y-intercept:
1) x - 5y = 7
-5y = -x + 7
y = 1/5x - 7/5
2) 3x - 2y = -4
-2y = -3x - 4
y = 3/2x + 2
Now, graphing these two equations we get two lines. The intersection point of the lines will be the solution to the system. By solving the two equations simultaneously, we can find the point of intersection:
1/5x - 7/5 = 3/2x + 2
1/5x - 3/2x = 2 + 7/5
-7/10x = 17/5
x = -17/7
Now, substitute x back into one of the equations to find the y-coordinate:
y = 1/5(-17/7) - 7/5
y = -17/35 - 7/5
y = -17/35 - 49/35
y = -66/35
y = -6/5
So, the solution to the system of equations x - 5y = 7 and 3x - 2y = -4 is (-17/7, -6/5), or approximately (-2.43, -1.2). The intersection point is (-2.43, -1.2).