Solve x+2y=7 (1)
X=4-2y (2)
Elimination
4x+5y=4
8x+10y=8 what is solution
There is no solution for either pair.
x = 7 - 2y
x = 4 - 2y
When multiplied by 2, 4x + 5y = 4 becomes
8x + 10y = 8
To solve the system of equations using the elimination method, we need to eliminate one of the variables by multiplying one or both of the equations by appropriate constants.
Let's start by multiplying equation (2) by 2 to eliminate the x term:
2(x) + 2(4 - 2y) = 2(4)
2x + 4 - 4y = 8
2x - 4y = 4 -> Equation (3)
Now, we have two equations:
Equation (1): x + 2y = 7
Equation (3): 2x - 4y = 4
Next, we can eliminate the y term by multiplying equation (1) by 2:
2(x + 2y) = 2(7)
2x + 4y = 14 -> Equation (4)
Now, we have two equations:
Equation (4): 2x + 4y = 14
Equation (3): 2x - 4y = 4
By adding equation (4) and equation (3), we can eliminate the y term:
(2x + 4y) + (2x - 4y) = 14 + 4
4x = 18
Dividing both sides of the equation by 4:
4x/4 = 18/4
x = 4.5
Now, we can substitute the value of x into one of the original equations to solve for y. Let's use equation (1):
x + 2y = 7
4.5 + 2y = 7
Subtracting 4.5 from both sides of the equation:
2y = 7 - 4.5
2y = 2.5
Dividing both sides of the equation by 2:
2y/2 = 2.5/2
y = 1.25
Therefore, the solution to the system of equations is x = 4.5 and y = 1.25.