-x+7y=5,-4x+y=-7 System of equations substitution

Mathematics

1 answer:

Leno4ka [110]3 years ago

5 0

Answer:

Step-by-step explanation:

$\left\{\begin{array}{ccc}-x+7y=5\\-4x+y=-7&\text{add}\ 4x\ \text{to both sides}\end{array}\right\\\\\left\{\begin{array}{ccc}-x+7y=5&(1)\\y=4x-7&(2)\end{array}\right\qquad\text{subtritute (2) to (1)}\\\\-x+7(4x-7)=5\qquad\text{use the distributive property}\\\\-x+(7)(4x)+(7)(-7)=5\\\\-x+28x-49=5\qquad\text{add 49 to both sides}\\\\-x+28x=5+49\qquad\text{combine like terms}\\\\27x=54\qquad\text{divide both sides by 27}\\\\\boxed{x=2}$

$\text{Put the value of}\ x\ \text{to (2):}\\\\y=4(2)-7\\\\y=8-7\\\\\boxed{y=1}$

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Question 1 (3 points) What value of p makes this equation true? 3p - 8 = -23 . O p = -6 Op = -5 Op = 5 p = 6

olchik [2.2K]

The value of p that makes the given equation true is equal to: B. p = -5

<u>Given the following equation:</u>

$3p - 8 = -23$

To find a value of p that makes the given equation true:

In this exercise, you're required to determine a value of p that satisfies the given equation true such that when substituted into the equation, it has a true result or outcome.

Rearranging the equation by collecting like terms, we have:

$3p - 8 = -23\\\\3p=-23+8\\\\3p=-15\\\\p=\frac{-15}{3}$