Review the graphs of a system of two linear equations in two variables: x-5y=7 and 3x-2y=-4. Find the solution to both equations. The interception point is (___)
To review the graphs of a system of two linear equations, we need to solve both equations and find their intersection point.
The given equations are:
1) x - 5y = 7
2) 3x - 2y = -4
Let's solve the equations using the elimination method:
First, let's multiply equation 1 by 2 to eliminate the x term:
2(x - 5y) = 2(7)
2x - 10y = 14
Now, we can subtract this new equation from the second equation:
(3x - 2y) - (2x - 10y) = -4 - 14
3x - 2y - 2x + 10y = -18
x + 8y = -18 ---> Equation 3
Now we have a new equation, let's write it down with equation 1:
x - 5y = 7 ---> Equation 1
x + 8y = -18 ---> Equation 3
Now, let's multiply equation 1 by 8, and equation 3 by 5, to eliminate the x term:
8(x - 5y) = 8(7)
5(x + 8y) = 5(-18)
Simplifying:
8x - 40y = 56 ---> Equation 4
5x + 40y = -90 ---> Equation 5
Now we can add equation 4 with equation 5:
(8x - 40y) + (5x + 40y) = 56 + (-90)
8x + 5x - 40 y + 40y = -34
13x = -34
Dividing both sides by 13:
x = -34/13
Now, let's substitute the value of x into equation 1 to find y:
-34/13 - 5y = 7
-34 - 65y = 91
-65y = 91 + 34
-65y = 125
y = 125/-65
y = -25/13
Therefore, the solution to the system of equations is (x, y) = (-34/13, -25/13).
The intersection point is (-34/13, -25/13).