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.

Answer 1

To review the graphs of the system of equations, we can plot the two equations on a graph.

The first equation, y = 4x - 10, is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. From the equation, we can see that the slope is 4, meaning that for every increase of 1 in x, there will be an increase of 4 in y. The y-intercept is -10, meaning that the graph will intersect the y-axis at y = -10.

The second equation, y = -2x + 8, is also in slope-intercept form. In this case, the slope is -2, meaning that for every increase of 1 in x, there will be a decrease of 2 in y. The y-intercept is 8, meaning that the graph will intersect the y-axis at y = 8.

To find the solution of the system, we need to find the point where the two graphs intersect. We can do this by setting the equations equal to each other and solving for x.

4x - 10 = -2x + 8
Adding 2x to both sides: 6x - 10 = 8
Adding 10 to both sides: 6x = 18
Dividing by 6 on both sides: x = 3

Now that we have the value of x, we can substitute it back into either equation to find y.

Using the first equation, y = 4(3) - 10 = 12 - 10 = 2

Therefore, the solution to the system of equations is x = 3, y = 2.