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. (1 point) The intersection point is (
3, -2)
To find the solution to both equations, we can solve the system of linear equations using the method of elimination.
First, let's rewrite the equations in slope-intercept form (y = mx + b):
Equation 1: x - 5y = 7
Rewriting in slope-intercept form, we get:
-5y = -x + 7
y = (1/5)x - 7/5
Equation 2: 3x - 2y = -4
Rewriting in slope-intercept form, we get:
-2y = -3x - 4
y = (3/2)x + 2
Now, let's graph the equations to find the intersection point.
For the first equation, y = (1/5)x - 7/5, we can start by plotting the y-intercept at -7/5 (the point (0, -7/5)). Then, we can use the slope of 1/5 to find another point. Since the slope is positive, we can move 5 units to the right and 1 unit up from the y-intercept point to get another point (5, -6/5). Now, we can draw a line passing through these two points.
For the second equation, y = (3/2)x + 2, we can again start by plotting the y-intercept at 2 (the point (0, 2)). Then, using the slope of 3/2, we can move 2 units to the right and 3 units up from the y-intercept point to get another point (2, 5). Now, we can draw a line passing through these two points.
The graphs of these two lines will intersect at a point, which represents the solution to the system of equations.
(Please note that the intersection point coordinates were cut off in your initial question.
To find the solution to a system of linear equations, you need to find the point(s) where the graphs of the equations intersect. In this case, let's start by graphing the system of equations:
Equation 1: x - 5y = 7
Equation 2: 3x - 2y = -4
To graph each equation, you can rearrange them into the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
For Equation 1, x - 5y = 7:
-5y = -x + 7
y = (1/5)x - (7/5)
For Equation 2, 3x - 2y = -4:
-2y = -3x - 4
y = (3/2)x + 2
Now, you can plot the graphs of both equations on the same graph. Looking at the slopes and intercepts, you 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.
The graph of the first equation is a line that passes through (-7/5, 0) and has a positive slope. The graph of the second equation is a line that passes through (0, 2) and has a steeper positive slope.
Now, find the point(s) where the two lines intersect. This is the solution to the system of equations. In this case, the intersection point is:
Solution: (2, 1)
Therefore, the solution to the system of equations x - 5y = 7 and 3x - 2y = -4 is (2, 1).