Given the following system of equations:3𝑥−2𝑦=73x−2y=7𝑥+𝑦=−1x+y=−1Solve to find the solution to the system.
Question
Given the following system of equations:3𝑥−2𝑦=73x−2y=7𝑥+𝑦=−1x+y=−1Solve to find the solution to the system.
Solution
To solve the system of equations, we can use either substitution or elimination method. Here, we will use the substitution method.
The system of equations is:
- 3x - 2y = 7
- x + y = -1
First, we can solve the second equation for x:
x = -1 - y
Then, we substitute x in the first equation:
3(-1 - y) - 2y = 7 -3 - 3y - 2y = 7 -5y - 3 = 7 -5y = 10 y = -2
Substitute y = -2 into the second equation:
x + (-2) = -1 x = 1
So, the solution to the system of equations is x = 1, y = -2.
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