Question

The system of linear equations −3x + 2y = −6 and y equals negative one half times x plus 4 is graphed on a coordinate plane. Approximate the solution to the system. coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 3 and another line that passes through the points 4 comma 3 and 0 comma negative 3

Answer 1

To approximate the solution to the system, we need to find the point where the two lines intersect. We can do this by solving the system of equations:

-3x + 2y = -6
y = -1/2x + 4

Substituting y = -1/2x + 4 into the first equation gives:

-3x + 2(-1/2x + 4) = -6

Simplifying this equation gives:

-4x + 8 = -6

Solving for x gives:

x = 7/4

Substituting x = 7/4 into the second equation gives:

y = -1/2(7/4) + 4

Simplifying this equation gives:

y = 9/4

Therefore, the system has a solution at the point (7/4, 9/4).

Regarding the second part of your prompt, we can find the equation for the line passing through the points (0, 4) and (2, 3) using the slope-intercept form of a line:

y - 4 = ((3 - 4)/(2 - 0))(x - 0)

Simplifying this equation gives:

y = -1/2x + 4

Similarly, we can find the equation for the line passing through the points (4, 3) and (0, -3):

y - 3 = ((-3 - 3)/(0 - 4))(x - 4)

Simplifying this equation gives:

y = 3/4x - 3

I hope this helps!