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 find the solution to the system of equations, let's first rewrite the equations in slope-intercept form (y = mx + b).
The first equation, x - 5y = 7, can be rewritten as:
-5y = -x + 7
y = (1/5)x - 7/5
The second equation, 3x - 2y = -4, can be rewritten as:
-2y = -3x - 4
y = (3/2)x + 2
Now that we have the equations in slope-intercept form, we can see that the first equation has a slope of 1/5 and a y-intercept of -7/5, while the second equation has a slope of 3/2 and a y-intercept of 2.
To find the intersection point, we need to find the x-coordinate where the two lines intersect. To do this, we can set the two equations equal to each other:
(1/5)x - 7/5 = (3/2)x + 2
Now we can solve for x:
(1/5)x - (3/2)x = 2 + 7/5
(10/50)x - (75/50)x = 10/5 + 7/5
(-65/50)x = 17/5
x = - (17/5) * (50/65)
x = -10/3
Now that we know the x-coordinate at which the two lines intersect, we can substitute this value into either of the original equations to find the y-coordinate. Let's use the first equation:
x - 5y = 7
-(10/3) - 5y = 7
-10 - 15y = 21
-15y = 21 + 10
-15y = 31
y = 31/-15
y = -31/15
Therefore, the solution to the system of equations is x = -10/3 and y = -31/15. The intersection point is (-10/3, -31/15).