Instructions: Solve each system by substitution. Make sure to check your answer BEFORE submitting. State your answer as an ordered pair. DO NOT include spaces in your answer.System 1y=−5x+13𝑦=−5𝑥+13y=−2x+7𝑦=−2𝑥+7(( ,, ))System 2y=−4x−12𝑦=−4𝑥−12y=7x+21𝑦=7𝑥+21(( ,, )
Question
Instructions: Solve each system by substitution. Make sure to check your answer BEFORE submitting. State your answer as an ordered pair. DO NOT include spaces in your answer.System 1y=−5x+13𝑦=−5𝑥+13y=−2x+7𝑦=−2𝑥+7(( ,, ))System 2y=−4x−12𝑦=−4𝑥−12y=7x+21𝑦=7𝑥+21(( ,, )
Solution
System 1:
Given the equations:
- y = -5x + 13
- y = -2x + 7
We can substitute equation 2 into equation 1, so wherever we see 'y' in equation 1, we replace it with '-2x + 7'. This gives us:
-2x + 7 = -5x + 13
Solving for x, we get:
5x - 2x = 13 - 7 3x = 6 x = 6 / 3 x = 2
Substitute x = 2 into equation 1:
y = -5(2) + 13 y = -10 + 13 y = 3
So, the solution to System 1 is (2, 3).
System 2:
Given the equations:
- y = -4x - 12
- y = 7x + 21
We can substitute equation 2 into equation 1, so wherever we see 'y' in equation 1, we replace it with '7x + 21'. This gives us:
7x + 21 = -4x - 12
Solving for x, we get:
4x + 7x = -12 - 21 11x = -33 x = -33 / 11 x = -3
Substitute x = -3 into equation 1:
y = -4(-3) - 12 y = 12 - 12 y = 0
So, the solution to System 2 is (-3, 0).
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