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. What’s the answer

Answer 1

To find the solution to both equations, we need to first graph the system of equations.

1. Graph of x - 5y = 7:
To graph this equation, we will first find its x-intercept and y-intercept.
x-intercept:
Set y = 0 in the equation x - 5y = 7:
x - 5(0) = 7
x = 7
So the x-intercept is at (7, 0).
y-intercept:
Set x = 0 in the equation x - 5y = 7:
0 - 5y = 7
-5y = 7
y = -7/5
So the y-intercept is at (0, -7/5).
Plot these two points and draw a line passing through them.

2. Graph of 3x - 2y = -4:
Similarly, find the x-intercept and y-intercept of this equation.
x-intercept:
Set y = 0 in the equation 3x - 2y = -4:
3x - 2(0) = -4
3x = -4
x = -4/3
So the x-intercept is at (-4/3, 0).
y-intercept:
Set x = 0 in the equation 3x - 2y = -4:
3(0) - 2y = -4
-2y = -4
y = 2
So the y-intercept is at (0, 2).
Plot these two points and draw a line passing through them.

The solution to the system of equations is the point where the two lines intersect. By visually inspecting the graph, we can see that the intersection point is approximately (1, -2).

Therefore, the solution to the system of equations x - 5y = 7 and 3x - 2y = -4 is x = 1 and y = -2.