Question

Review the graphs of a system of these two linear equations in two variables: y=4x−10 and y=−2x+8 Find the solution of the system. (1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the solution of the system, we can start by graphing the two linear equations and identifying the point at which they intersect.

First, let's graph the equation y=4x−10.

To graph this equation, we can start by plotting two or more points on the line. We can choose any values for x, substitute them into the equation, and solve for y.

Let's choose x = 0:
y = 4(0) - 10
y = -10
So, one point on the line is (0, -10).

Let's choose x = 3:
y = 4(3) - 10
y = 12 - 10
y = 2
So, another point on the line is (3, 2).

We can now plot these two points on a coordinate plane and draw a straight line passing through them.

Next, let's graph the equation y=−2x+8.

Using the same process, we can choose values for x, substitute them into the equation, and solve for y.

Let's choose x = 0:
y = -2(0) + 8
y = 8
So, one point on the line is (0, 8).

Let's choose x = 4:
y = -2(4) + 8
y = -8 + 8
y = 0
So, another point on the line is (4, 0).

Plotting these two points on the coordinate plane and drawing a straight line passing through them gives us:

The solution of the system is the point at which the two lines intersect, which in this case is approximately (2, -2).

Therefore, the solution of the system is (2, -2).