Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.
-3x – 5y = 61
7x – 5y = -9
Eq1: -3X - 5Y = 61
Eq2: 7X - 5Y = -9
Multiply both sides of Eq1 by -1 and
add the 2 Eqs:
3X + 5Y = -61
7X - 5Y = -9
Sum: 10X = -70,
X = -70 / 10 = -7.
Substitute -7 for x in Eq2:
7*-7 - 5Y = -9,
-49 - 5Y = -9,
-5Y = -9 + 49 = 40,
Y = 40 / -5 = -8.
Solution set = (-7, -8).
To solve the system of equations using the elimination method, we need to eliminate one variable by adding or subtracting the equations. In this case, we can eliminate the variable "y" by multiplying the second equation by -1 and then adding it to the first equation.
First, let's multiply the second equation by -1:
-1(7x - 5y) = -1(-9)
-7x + 5y = 9
Now, add the two equations together:
(-3x - 5y) + (-7x + 5y) = 61 + 9
-3x - 7x - 5y + 5y = 70
-10x = 70
Divide both sides of the equation by -10:
-10x/-10 = 70/-10
x = -7
Now that we have the value of x, substitute it back into one of the original equations to solve for y. Let's use the first equation:
-3x - 5y = 61
-3(-7) - 5y = 61
21 - 5y = 61
To isolate y, subtract 21 from both sides of the equation:
21 - 21 - 5y = 61 - 21
-5y = 40
Divide both sides of the equation by -5:
-5y/-5 = 40/-5
y = -8
So, the solution to the system of equations is x = -7 and y = -8.