Estimate the intersection point of the graphs of the following linear equations in two variables. y=−x+7 y=4x−3
To find the intersection point, we can set the two equations equal to each other and solve for x.
Starting with the given equations:
y = -x + 7 ...(equation 1)
y = 4x - 3 ...(equation 2)
Setting equation 1 equal to equation 2:
-x + 7 = 4x - 3
Next, we can add x to both sides of the equation, and subtract 7 from both sides:
7 - 3 = 4x + x
Simplifying:
4 = 5x
Finally, we can divide both sides by 5 to solve for x:
x = 4/5
Now, we can substitute this value of x back into either equation 1 or equation 2 to find the corresponding value of y. Let's use equation 1:
y = -(4/5) + 7
Simplifying:
y = -(4/5) + 35/5
y = (35-4)/5
y = 31/5
Therefore, the estimated intersection point of the graphs is (4/5, 31/5).
To find the intersection point of two linear equations, we need to solve the system of equations simultaneously. In this case, the given equations are:
Equation 1: y = -x + 7
Equation 2: y = 4x - 3
To find the intersection point, we'll substitute one equation into the other. Let's substitute Equation 1 into Equation 2:
- x + 7 = 4x - 3
Now, let's solve for x:
- x - 4x = -3 - 7
-5x = -10
x = -10 / -5
x = 2
We have found the x-coordinate of the intersection point. Now, let's substitute this value into one of the original equations (let's use Equation 1) to find the y-coordinate:
y = -x + 7
y = -(2) + 7
y = 5
Therefore, the intersection point of the given linear equations is (2, 5).
To find the intersection point of the two linear equations, we need to solve them simultaneously. Since both equations are already solved for y, we can equate them:
−x + 7 = 4x − 3
Let's solve for x now:
Adding x to both sides, we get:
7 = 5x − 3
Adding 3 to both sides, we get:
10 = 5x
Dividing both sides by 5, we get:
2 = x
Now that we know the value of x, we can substitute it back into either equation to find the corresponding y.
Let's use the first equation:
y = -(2) + 7
y = -2 + 7
y = 5
Therefore, the intersection point of the two linear equations is (2, 5).