Solve the system of equations using the substitution method. State your final answer as an ordered pair. DO NOT include spaces in your answer.y=7x−9𝑦=7𝑥−9y=−2x+9𝑦=−2𝑥+9Solution:
Question
Solve the system of equations using the substitution method. State your final answer as an ordered pair. DO NOT include spaces in your answer.y=7x−9𝑦=7𝑥−9y=−2x+9𝑦=−2𝑥+9Solution:
Solution
First, we have two equations:
- y = 7x - 9
- y = -2x + 9
We can use the substitution method to solve this system of equations. This method involves solving one of the equations for one variable in terms of the other variable, then substituting this expression into the other equation.
From equation 1) we have y in terms of x, so we can substitute this into equation 2):
7x - 9 = -2x + 9
Now, we can solve for x:
Add 2x to both sides: 7x + 2x = 9 + 9 Simplify: 9x = 18 Divide by 9: x = 2
Now that we have x, we can substitute x = 2 into the first equation to solve for y:
y = 7(2) - 9 y = 14 - 9 y = 5
So, the solution to the system of equations is (2,5).
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