Solve using the elimination method? 4x-9y=6.5 AND 7Y-2X=4.5
doulble the second equation, then add equations. It might be a tad clearer if you change the second equation to have the x first, as in -2x+7y=4.5
thanks.
To solve the system of equations using the elimination method, we need to eliminate one variable so that we can solve for the other.
Let's start by eliminating the variable y. Multiply the second equation by 9 to make the coefficients of y in both equations the same:
9 * (7y - 2x) = 9 * 4.5
63y - 18x = 40.5
Now, we can add the two equations together to eliminate y:
4x - 9y + (63y - 18x) = 6.5 + 40.5
Simplifying the left side of the equation:
4x - 18x - 9y + 63y = 47
Combine like terms:
-14x + 54y = 47
Now, we have one equation with only x and y. We can solve for one variable and use that value to find the other variable. Let's solve for x:
-14x = 47 - 54y
x = (47 - 54y) / -14 ----- (Equation 1)
Now, let's solve for y by substituting the value of x from Equation 1 into one of the original equations. Let's use the first equation:
4((47 - 54y) / -14) - 9y = 6.5
Simplifying and getting rid of the fraction:
(47 - 54y) / -3.5 - 9y = 6.5
Multiply both sides of the equation by -3.5 to clear the fraction:
47 - 54y - 31.5y = -22.75
Combine like terms:
-85.5y = -22.75 - 47
-85.5y = -69.75
y = -69.75 / -85.5
y ≈ 0.814
Now that we have the value of y, we can substitute it back into Equation 1 to find x:
x = (47 - 54(0.814)) / -14
x ≈ -1.5
Therefore, the solution to the system of equations is x ≈ -1.5 and y ≈ 0.814.