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
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).
To find the intersection point of the system of linear equations, we need to solve the equations simultaneously.
Given the two equations:
1) y = 4x - 10
2) y = -2x + 8
We can set the equations equal to each other to get:
4x - 10 = -2x + 8
Now, let's simplify and solve for x:
4x + 2x = 8 + 10
6x = 18
x = 3
Now that we have the value of x, we can substitute it back into either of the equations to find the y-coordinate. Let's use equation 1:
y = 4x - 10
y = 4(3) - 10
y = 12 - 10
y = 2
Therefore, the intersection point of the two linear equations is (3, 2).