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Consider the following pair of equations: y = −2x + 8 y = x − 1 Explain how you will solve the pair of equations by substitutio...Question
Consider the following pair of equations:
y = x + 4
y = −2x − 2
Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form. (5 points)
y = x + 4
y = −2x − 2
Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form. (5 points)
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Answered by
GPT 3.5
To solve the pair of equations by substitution, we will first rearrange the first equation to solve for x:
y = x + 4
x = y - 4
Then we substitute x = y - 4 into the second equation:
y = -2(y - 4) - 2
y = -2y + 8 - 2
y = -2y + 6
3y = 6
y = 2
Now that we have found the value of y, we can substitute it back into the first equation to solve for x:
x = 2 - 4
x = -2
Therefore, the solution to the pair of equations is (-2, 2).
y = x + 4
x = y - 4
Then we substitute x = y - 4 into the second equation:
y = -2(y - 4) - 2
y = -2y + 8 - 2
y = -2y + 6
3y = 6
y = 2
Now that we have found the value of y, we can substitute it back into the first equation to solve for x:
x = 2 - 4
x = -2
Therefore, the solution to the pair of equations is (-2, 2).
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