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 review the graphs of the system of equations, we can first graph each equation separately.

For the equation y = 4x - 10, we can start by finding the y-intercept, which is -10. This means that the point (0, -10) lies on the line. We can also find the x-intercept by setting y = 0 and solving for x:

0 = 4x - 10
4x = 10
x = 10/4
x = 2.5

So, the x-intercept is (2.5, 0).

We can then connect the y-intercept (-10) and the x-intercept (2.5) with a straight line. This line has a positive slope of 4, which means it rises 4 units for every 1 unit it moves to the right.

For the equation y = -2x + 8, we find the y-intercept by setting x = 0:

y = -2(0) + 8
y = 8

So, the y-intercept is (0, 8).

We can also find the x-intercept by setting y = 0 and solving for x:

0 = -2x + 8
2x = 8
x = 8/2
x = 4

So, the x-intercept is (4, 0).

We can then connect the y-intercept (8) and the x-intercept (4) with a straight line. This line has a negative slope of -2, which means it falls 2 units for every 1 unit it moves to the right.

Now we can analyze the graphs together. The first line has a positive slope and the second line has a negative slope. As a result, the lines are not parallel and they will intersect at a single point which represents the solution of the system of equations.

To find the solution, we can set the two equations equal to each other:

4x - 10 = -2x + 8

Adding 2x to both sides:

6x - 10 = 8

Adding 10 to both sides:

6x = 18

Dividing both sides by 6:

x = 3

Substituting this value of x back into one of the original equations, we can solve for y:

y = -2(3) + 8

y = 8 - 6

y = 2

Therefore, the solution of the system of equations is (3, 2).