Solve using the substitution method. Show your work. If the system has no solution or an infinite number of solutions, state this.
18x + 6y = 78
12x + 54y = -48
y = 13 - 3x (from the first equation)
Substitute that for y in the second equation, and solve for x.
12x + 54*13 - 162x = -48
150 x = 750
Take it from there.
48 divided by 2(9+3)=
parent needs answer.... i came up up with answer of 2
son has different answer of 288
To solve the given system of equations using the substitution method, we have to solve one of the equations for one variable and then substitute it into the other equation. Let's start by solving the first equation for x.
Equation 1: 18x + 6y = 78
Step 1: Isolate x by subtracting 6y from both sides:
18x = 78 - 6y
Step 2: Divide both sides by 18 to solve for x:
x = (78 - 6y) / 18
Simplifying:
x = (13 - y/3)
Now that we have x in terms of y, we can substitute this expression into the second equation.
Equation 2: 12x + 54y = -48
Substituting x = 13 - y/3 into Equation 2:
12(13 - y/3) + 54y = -48
Step 3: Distribute 12 to the terms within parentheses:
156 - 4y + 54y = -48
Step 4: Combine like terms:
50y + 156 = -48
Step 5: Subtract 156 from both sides:
50y = -48 - 156
50y = -204
Step 6: Divide both sides by 50 to solve for y:
y = -204/50
y = -4.08
Now, substitute the value of y back into x = 13 - y/3 to find the value of x:
x = 13 - (-4.08)/3
x = 13 + 1.36
x = 14.36
Therefore, the solution to the system of equations is x = 14.36 and y = -4.08.
There is only one solution to this system of equations, so it doesn't have an infinite number of solutions or no solution.