5x-4y=10
2x+8y=4
X = 2
Y = -2.5
Slope = 1.250
Eq1: 5x - 4y = 10.
Eq2: 2x + 8y = 4.
Multiply Eq1 by 2 and add the Eqs:
10x - 8y = 20.
+2x + 8y = 4.
Sum: 12x = 24,m X = 2.
In Eq2, replace x with 2:
2*2 + 8y = 4. Y = 0.
M1 = -A/B = -5/-4 = 1.25.
M2 = -2/8 = -0.25.
To solve this system of equations, we can use the method of elimination. The goal is to eliminate one of the variables by multiplying one or both of the equations by appropriate constants, and then adding or subtracting the equations to eliminate that variable.
Let's start by multiplying the first equation by 4, and the second equation by -1 to eliminate the y variable:
4 * (5x - 4y) = 4 * 10
-1 * (2x + 8y) = -1 * 4
This simplifies the equations to:
20x - 16y = 40
-2x - 8y = -4
Now, let's add the two equations together:
(20x - 16y) + (-2x - 8y) = 40 + (-4)
This simplifies to:
18x - 24y = 36
Now we have one equation with just the x variable and one equation with just the y variable. We can solve one equation for one variable and substitute it into the other equation to find the values of x and y.
Let's solve the second equation for x:
-2x = -4 + 8y
x = (4 - 8y) / -2
x = -2y + 2
Now we substitute this value of x into the first equation:
18(-2y + 2) - 24y = 36
Simplifying:
-36y + 36 - 24y = 36
-60y = 0
y = 0
Now we substitute the value of y = 0 into the equation we obtained for x:
x = -2(0) + 2
x = 2
Therefore, the solution to the system of equations is x = 2 and y = 0.