2x+11y=9
4x-8y=0
how do I solve this system of equations?
Multiply first equation by two.
4x + 22y = 9
4x - 8y = 0
Subtract second equation from first.
30y = 9
y = 9/30 = 3/10 = .3
To solve this system of equations, you can use either the substitution method or the elimination method. Let's use the elimination method:
Step 1: Multiply the first equation by 2 and the second equation by 4 to make the coefficients of x in both equations the same:
2(2x + 11y = 9) --> 4x + 22y = 18
4(4x - 8y = 0) --> 16x - 32y = 0
Step 2: Now subtract the second equation from the first equation to eliminate x:
(4x + 22y) - (16x - 32y) = 18 - 0
4x + 22y - 16x + 32y = 18
-12x + 54y = 18
Step 3: Simplify the equation:
-12x + 54y = 18 --> -2x + 9y = 3 (divide each term by 6)
So, the new system of equations is:
-2x + 9y = 3 (Equation 1)
4x - 8y = 0 (Equation 2)
Now we have a new system of equations with simpler coefficients. We can proceed to solve this system by either the substitution or elimination method.
To solve the system of equations, you can use the method of substitution or elimination. Let's use the method of substitution for this example:
1. Start by solving one equation for one variable in terms of the other variable. Let's solve the first equation for x in terms of y:
2x + 11y = 9
2x = 9 - 11y
x = (9 - 11y) / 2
2. Substitute this expression for x into the second equation:
4x - 8y = 0
4((9 - 11y) / 2) - 8y = 0
Simplify the expression:
18 - 22y - 8y = 0
Combine like terms:
-30y + 18 = 0
-30y = -18
y = -18 / -30
y = 3/5
3. Now that you have the value of y, substitute it back into either equation to find the value of x. Let's use the first equation:
2x + 11(3/5) = 9
2x + 33/5 = 9
2x = 9 - 33/5
2x = (45 - 33) / 5
2x = 12 / 5
x = 12 / (2 * 5)
x = 12 / 10
x = 6 / 5
So the solution to the system of equations is x = 6/5 and y = 3/5.