. Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.
-2x + 9y = 56
9x – 9y = 0
-2x + 9y = 56
9x – 9y = 0
Add these two equations
7x + 0y = 56
7x = 56
x = 8
Substitute x = 8 in either equation to find y.
Then check your solution for x and y in the original equation(s).
Determine whether the point (0, 8) is a solution of the system
-3x + 9y = 72 / 9x + 3y = 24
To solve this system of equations using the elimination method, we need to eliminate one variable by adding or subtracting the two equations. Let's proceed step-by-step:
Step 1: Multiply the second equation by -1 to make the coefficients of y in both equations cancel each other out.
-2x + 9y = 56 (Equation 1)
-1 * (9x - 9y) = -1 * 0
-9x + 9y = 0 (Equation 2)
Rewriting the second equation after multiplying by -1:
-9x + 9y = 0 (Equation 2')
Step 2: Add Equation 1 and Equation 2' to eliminate x.
-2x + 9y + (-9x + 9y) = 56 + 0
Combining like terms:
-2x - 9x + 9y + 9y = 56
Simplifying:
-11x + 18y = 56
Now we have a single equation with only two variables.
Step 3: Try solving the equation.
-11x + 18y = 56
Since we still have two variables, we cannot uniquely solve for x or y. Therefore, the system of equations has no solution.
In conclusion, the system of equations -2x + 9y = 56 and 9x – 9y = 0 has no solution.