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.
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.
To find the solution of the system of two linear equations, we can first graph the equations and then find the point where the two lines intersect. This intersection point represents the solution to the system.
Let's start by graphing the first equation, y = 4x - 10. To do this, we can plot a few points and connect them to form a line.
1. Choose a value for x, let's say x = 0. Plug this value into the equation to find the corresponding y-value:
y = 4(0) - 10
y = 0 - 10
y = -10
So, we have the point (0, -10).
2. Choose another value for x, let's say x = 3:
y = 4(3) - 10
y = 12 - 10
y = 2
So, we have another point (3, 2).
Plot these points on a graph and connect them to form a line. This line represents the first equation.
Next, let's graph the second equation, y = -2x + 8. Again, we can choose x-values and find the corresponding y-values to plot points on the graph.
1. For x = 0:
y = -2(0) + 8
y = 0 + 8
y = 8
So, the point is (0, 8).
2. For x = 3:
y = -2(3) + 8
y = -6 + 8
y = 2
So, another point is (3, 2).
Plot these points and connect them to form a line. This line represents the second equation.
Now, we can observe the graph and find the intersection point. The solution to the system of equations is the x-coordinate and y-coordinate of this point.
Based on the graph, it's evident that the two lines intersect at the point (3, 2) which means x = 3 and y = 2. Therefore, the solution to the system of equations is x = 3 and y = 2.