Estimate the intersection point of the graphs of the following linear equation in two variables. Y = x + 2 are y = -x + 6
To find the intersection point of the two graphs, we need to solve the system of equations:
y = x + 2
y = -x + 6
Setting the two equations equal to each other gives:
x + 2 = -x + 6
Solving for x, we get:
2x = 4
x = 2
Now that we have found the value of x, we can substitute it back into one of the original equations to find the value of y. Let's use the first equation:
y = 2 + 2
y = 4
Therefore, the intersection point of the two graphs is (2, 4).
Review the graph of a system of two linear equations and two variables: 4x + 3y = 15 and y = x + 5.
To review the graph of the system of equations 4x + 3y = 15 and y = x + 5, we can first rewrite the equations in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
For the equation 4x + 3y = 15:
3y = -4x + 15
y = (-4/3)x + 5
For the equation y = x + 5, it is already in slope-intercept form with a slope of 1 and a y-intercept of 5.
Now, let's graph both equations on the same coordinate system to see where they intersect:
The first equation, y = (-4/3)x + 5, has a y-intercept of 5 and a slope of -4/3. This means that the line will intersect the y-axis at the point (0, 5) and slope downwards to the right.
The second equation, y = x + 5, has a y-intercept of 5 and a slope of 1. This line intersects the y-axis at the point (0, 5) and slopes upwards to the right.
By graphing these two lines, we can see that they intersect at the point (3, 8). This is the solution to the system of equations 4x + 3y = 15 and y = x + 5.