How would you solve the systemof equations using the substitution method:
2x-9y=2
4x+18y=12
Take the first equation and solve for x:
2x-9y=2
x=(2+9y)/2
Substitute this value of x into the second equation and solve for y.
Substitute the solution for y into the first equation to find the solution of x.
BACK SUBSTITUTE x and y into both equations to make sure the answer is correct.
how would you solve this prblem n+37 if n is 16
To solve this system of equations using the substitution method, follow these steps:
Step 1: Solve one equation for one variable in terms of the other variable.
Let's start with the first equation, 2x - 9y = 2. Solve this equation for x.
2x - 9y = 2
2x = 9y + 2
x = (9y + 2)/2
x = (9/2)y + 1
So, we have x in terms of y: x = (9/2)y + 1.
Step 2: Substitute the expression for x from Step 1 into the second equation.
The second equation is 4x + 18y = 12. Substitute x = (9/2)y + 1 into this equation:
4((9/2)y + 1) + 18y = 12
Step 3: Simplify and solve for y.
Multiplying through by 2 to get rid of the denominator:
4(9y + 2) + 36y = 24
36y + 8 + 36y = 24
72y + 8 = 24
72y = 16
y = 16/72
y = 2/9
Step 4: Substitute the value of y back into x = (9/2)y + 1 to solve for x.
x = (9/2)(2/9) + 1
x = 1 + 1
x = 2
Step 5: Check the solution by substituting the values of x and y into both original equations.
Substituting x = 2 and y = 2/9 into the first equation, we get:
2(2) - 9(2/9) = 2
4 - 2 = 2
2 = 2 (True)
Substituting x = 2 and y = 2/9 into the second equation, we get:
4(2) + 18(2/9) = 12
8 + 4 = 12
12 = 12 (True)
Both equations are satisfied by the values x = 2 and y = 2/9, so the solution to the system of equations is x = 2 and y = 2/9.