Estimate the intersection point of the graphs of the following linear equations in two variables. y=x+2 y=−x+6
To find the intersection point of two linear equations, we can set the equations equal to each other and solve for x.
So, x + 2 = -x + 6.
Combining like terms, we get 2x + 2 = 6.
Subtracting 2 from both sides, we have 2x = 4.
Dividing both sides by 2, we get x = 2.
To find the y-coordinate of the intersection point, we can substitute the value of x into either of the original equations. Let's use the first equation, y = x + 2.
Substituting x = 2, we get y = 2 + 2 = 4.
Therefore, the intersection point of the two graphs is (2, 4).
Estimate the intersection point of the graphs of the following linear equations in two variables. y=−x+7 y=4x−3
To estimate the intersection point of the two linear equations, let's plot the lines on a graph.
The first equation, y = -x + 7, has a y-intercept of 7 and a slope of -1. This means that for every increase of 1 in x, y decreases by 1. We can plot a point at (0, 7) and then use the slope to find another point. From (0, 7), we can move 1 unit to the right and 1 unit down to get (1, 6), and then repeat to get (2, 5).
The second equation, y = 4x - 3, has a y-intercept of -3 and a slope of 4. This means that for every increase of 1 in x, y increases by 4. We can plot a point at (0, -3) and then use the slope to find another point. From (0, -3), we can move 1 unit to the right and 4 units up to get (1, 1), and then repeat to get (2, 5).
Now, let's plot these points and draw the lines:
Graph:
|
7 | x +
| +
| +
| +
2 |+
|
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0 1 2 3 4
From the graph, we can estimate that the intersection point is approximately (2, 5).
To find the intersection point of the graphs of the given linear equations, we need to solve the system of equations:
y = x + 2 ----(1)
y = -x + 6 ----(2)
We can solve this system of equations by substituting the value of y from equation (2) into equation (1):
x + 2 = -x + 6
Now, let's solve for x:
2x = 4
x = 2
Substituting the value of x = 2 into equation (1):
y = 2 + 2
y = 4
Therefore, the intersection point of the given linear equations is (2, 4).
To find the intersection point of the graphs of two linear equations, we need to solve the system of equations. In this case, the equations are:
y = x + 2 (Equation 1)
y = -x + 6 (Equation 2)
To solve this system, we can equate the two equations by setting y in Equation 1 equal to y in Equation 2:
x + 2 = -x + 6
Now, let's solve for x:
2x = 4
x = 2
Next, substitute the value of x back into either of the equations to find the value of y. Let's use Equation 1:
y = x + 2
y = 2 + 2
y = 4
Therefore, the intersection point of the graphs of these two linear equations is (2, 4).