Solve by elimination
8x-9y=8.5
7y-2x=-4.5
Given
8X - 9Y = 8.5
7Y - 2X = 4.5
Rearrange 2nd Eq.
8X - 9Y = 8.5
-2X + 7Y = 4.5
Multiply 2nd Eq. by 4:
8X - 9Y = 8.5
-8X +28Y = 18
Add the 2 Eq.
19Y = 26.5
Solve for Y.
Y = 26.5/19 = 1.39
-2X +7(1.39) = 4.5, Solve for X:
X = 2.62
To solve the given system of equations by elimination, we can eliminate one of the variables by manipulating the equations and adding them together or subtracting them.
Let's eliminate the variable x by manipulating the equations:
Step 1: Rearrange the equations to have the same coefficient for x or y, making it easier to eliminate one of the variables.
The first equation:
8x - 9y = 8.5
The second equation:
-2x + 7y = -4.5
We can multiply the second equation by 4 to get the coefficients of x in both equations to be -8.
So, the second equation becomes:
-8x + 28y = -18
Step 2: Add the two equations together, eliminating x.
(8x - 9y) + (-8x + 28y) = (8.5) + (-18)
The x terms cancel out, leaving us with:
-9y + 28y = 8.5 - 18
Simplifying further gives us:
19y = -9.5
Step 3: Solve for y.
Divide both sides of the equation by 19:
(19y)/19 = (-9.5)/19
Simplifying:
y = -0.5
Step 4: Substitute the value of y back into one of the original equations to solve for x. Let's use the first equation.
8x - 9(-0.5) = 8.5
Simplifying:
8x + 4.5 = 8.5
Subtract 4.5 from both sides:
8x = 4
Divide both sides by 8:
(8x)/8 = 4/8
Simplifying further:
x = 0.5
The solution to the system of equations is x = 0.5 and y = -0.5.