Solve using the elimination method. If the system has no solution or an infinite number of solutions, state this.
10x - y = 12.5
3x + y = 7
To solve the system of equations using the elimination method, we need to eliminate one variable by adding or subtracting the equations. Let's start by adding the two equations:
(10x - y) + (3x + y) = 12.5 + 7
Combining like terms, we get:
13x = 19.5
Now, we can solve for x by dividing both sides of the equation by 13:
x = 1.5
Next, we substitute the value of x into one of the original equations to find the value of y. Let's use the second equation:
3(1.5) + y = 7
Simplifying this equation, we have:
4.5 + y = 7
Now, subtract 4.5 from both sides of the equation to isolate y:
y = 2.5
Therefore, the solution to the system of equations is x = 1.5 and y = 2.5.
In this case, the system has a unique solution.
Eq1: 10X - Y = 12.5.
Eq2: 3X + Y = 7.
Add the 2 Eqs and get:
13X + 0 = 19.5.
X = 1.5.
In Eq1, substitute 1.5 for X:
10*1.5 - Y = 12.5,
15 - Y = 12.5,
Y = 2.5.
Solution set: (X,Y) = (1.5,2.5).