5x-4y=10
-10x+2y=-20
What are the values of the x and y for both equations
multiply the second equation by 2
5 x - 4 y = 10
-20x +4 y = -40
------------------ mow add
-15 x = -30
x = 2 etc
What would y be? Is it 0
To find the values of x and y for the given system of equations, we will solve the system using the method of elimination.
1. Start by multiplying both sides of the first equation by 2 to eliminate the y term:
2*(5x-4y) = 2*(10)
10x - 8y = 20
2. Multiply both sides of the second equation by 5 to eliminate the x term:
5*(-10x + 2y) = 5*(-20)
-50x + 10y = -100
3. Now, add the two modified equations together to eliminate the x term:
(10x - 8y) + (-50x + 10y) = 20 + (-100)
-40x + 2y = -80
4. Simplify the equation:
2y - 40x = -80
5. Divide both sides of the equation by 2 to solve for y:
2y/2 - 40x/2 = -80/2
y - 20x = -40
Now we have the new equation: y - 20x = -40.
6. Let's call this new equation Equation (3) and compare it to Equation (1):
5x - 4y = 10 (Equation 1)
y - 20x = -40 (Equation 3)
7. Multiply Equation (3) by -4 to cancel out the y term:
-4*(y - 20x) = -4*(-40)
-4y + 80x = 160
8. Add Equation (1) and Equation (3) together:
(5x - 4y) + (-4y + 80x) = 10 + 160
5x - 4y - 4y + 80x = 170x = 170
9. Divide both sides of the equation by 170 to solve for x:
x = 170/170 = 1
Now we have the value of x as 1.
10. Substitute the value of x into Equation (1) to solve for y:
5(1) - 4y = 10
5 - 4y = 10
-4y = 10 - 5
-4y = 5
y = 5/(-4)
y = -5/4
The values of x and y for both equations are x = 1 and y = -5/4 (-1.25).