What would your first step look like if you were solving this system using the substitution method? DO NOT include spaces in your answer.y=x−10𝑦=𝑥−10 y=−6x+18𝑦=−6𝑥+18 == Now, finish solving the system of equations using the substitution method and state your final answer as an ordered pair.(( ,, )
Question
What would your first step look like if you were solving this system using the substitution method? DO NOT include spaces in your answer.y=x−10𝑦=𝑥−10 y=−6x+18𝑦=−6𝑥+18 == Now, finish solving the system of equations using the substitution method and state your final answer as an ordered pair.(( ,, )
Solution 1
The first step in solving this system using the substitution method would be to substitute the equation y = x - 10 into the second equation in place of y. This gives us:
x - 10 = -6x + 18
Now, to solve for x, we add 6x to both sides of the equation:
x + 6x = 18 + 10 7x = 28 x = 28 / 7 x = 4
Now that we have the value of x, we can substitute x = 4 into the first equation to solve for y:
y = 4 - 10 y = -6
So, the solution to the system of equations is the ordered pair (4, -6).
Solution 2
The first step in solving this system using the substitution method would be to substitute the equation y = x - 10 into the second equation in place of y. This gives us:
x - 10 = -6x + 18
Now, to solve for x, we can add 6x to both sides of the equation to get:
7x - 10 = 18
Then, add 10 to both sides to isolate 7x:
7x = 28
Finally, divide both sides by 7 to solve for x:
x = 4
Now that we have x, we can substitute x = 4 into the first equation to solve for y:
y = 4 - 10
So, y = -6
Therefore, the solution to the system of equations is the ordered pair (4, -6).
Solution 3
The first step in solving this system using the substitution method is to substitute the first equation into the second equation. This means wherever we see 'y' in the second equation, we replace it with 'x - 10'.
So, the second equation becomes: x - 10 = -6x + 18
Now, to solve for 'x', we need to get all the 'x' terms on one side of the equation and the constants on the other side.
Add 6x to both sides: x + 6x = 18 + 10 7x = 28
Divide by 7: x = 4
Now that we have the value of 'x', we can substitute it back into the first equation to find the value of 'y':
y = 4 - 10 y = -6
So, the solution to the system of equations is the ordered pair (4, -6).
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