Question

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 is wrong

Answer 1

To find the solution to both equations, we need to find the intersection point of the two lines represented by the equations.

To graph the first equation, x - 5y = 7, we can rewrite it in slope-intercept form (y = mx + b) by solving for y:
-5y = -x + 7
y = (1/5)x - 7/5

To graph the second equation, 3x - 2y = -4, we can also rewrite it in slope-intercept form:
-2y = -3x - 4
y = (3/2)x + 2

Now, we can plot the two lines on a coordinate plane:

Graph of the first equation (blue line represented by y = (1/5)x - 7/5):
-5y = -x + 7
y = (1/5)x - 7/5

Using the slope-intercept form, we start at the y-intercept (0, -7/5) and use the slope (1/5) to find another point. For example, we can move 5 units to the right (changing x) and 1 unit up (changing y). This gives us (5, -6/5). Now we can plot the two points and draw the line passing through them.

Graph of the second equation (red line represented by y = (3/2)x + 2):
-2y = -3x - 4
y = (3/2)x + 2

Using the slope-intercept form, we start at the y-intercept (0, 2) and use the slope (3/2) to find another point. For example, we can move 2 units to the right (changing x) and 3 units up (changing y). This gives us (2, 5). Now we can plot the two points and draw the line passing through them.

The lines intersect at the point (3, -2). So, the solution to both equations is x = 3 and y = -2.