Question

Review the graphs of a system of these two linear equations in two variables y = 4x -10 and y = -2x +8 find the intersection point

Answer 1

To find the intersection point of the two linear equations, we can set them equal to each other and solve for x.

So, let's set 4x - 10 = -2x + 8.

Adding 2x to both sides, we get 6x - 10 = 8.

Adding 10 to both sides, we get 6x = 18.

Dividing both sides by 6, we find x = 3.

Now, we can substitute this value back into either equation to solve for y. Let's use the first equation:

y = 4(3) - 10 = 12 - 10 = 2.

Therefore, the intersection point of the two linear equations is (3, 2).

To review the graphs of these two equations, let's plot them on a coordinate plane:

The first equation, y = 4x - 10, has a y-intercept of -10 and a slope of 4. The line will rise 4 units for every 1 unit it moves to the right.

The second equation, y = -2x + 8, has a y-intercept of 8 and a slope of -2. The line will fall 2 units for every 1 unit it moves to the right.

Plotting these two lines on the coordinate plane, we find that they intersect at the point (3,2).