Solve each system 3x-9y=3 and 2x=16-y
x = -1
y = -2/3
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To solve the system of equations 3x-9y=3 and 2x=16-y, we can use the method of substitution.
Step 1: Solve one equation for one variable in terms of the other variable.
From the second equation, 2x = 16-y, we can isolate y by subtracting 2x from both sides:
y = 16 - 2x
Step 2: Substitute the expression from Step 1 into the other equation.
Substituting y = 16 - 2x into the first equation, we have:
3x - 9(16 - 2x) = 3
Step 3: Simplify and solve for x.
Now, distribute the -9 to both terms inside the parentheses:
3x - 144 + 18x = 3
Combine like terms:
21x - 144 = 3
Add 144 to both sides of the equation:
21x = 147
Divide both sides by 21:
x = 7
Step 4: Substitute the value of x back into one of the original equations or equations in order to solve for y.
Using the second equation, 2x = 16 - y, we can substitute x = 7:
2(7) = 16 - y
14 = 16 - y
Subtract 16 from both sides of the equation:
-2 = -y
Multiply both sides by -1 to solve for y:
2 = y
Step 5: Check the solution.
Substitute the values of x and y into both original equations to verify that they satisfy both equations.
For the first equation, 3x - 9y = 3:
3(7) - 9(2) = 3
21 - 18 = 3
3 = 3
For the second equation, 2x = 16 - y:
2(7) = 16 - 2
14 = 14
The solution to the system of equations is x = 7 and y = 2.