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Zepler [3.9K]
3 years ago
10

Answers for the 2 boxes please:)​

Mathematics
1 answer:
masha68 [24]3 years ago
6 0

Answer:

(5,-5)

Step-by-step explanation:

<u>Eliminate</u><u> </u><u>y-term</u>

(2x + 5x) + ( - 3y + 3y) = 25 + 10 \\ 7x = 35 \\ x =  \frac{35}{7}  \\  x = 5

We can eliminate x-term but for this system of equations, eliminating y-term is faster.

<u>Substitute</u><u> </u><u>x</u><u> </u><u>=</u><u> </u><u>5</u><u> </u><u>in</u><u> </u><u>any</u><u> </u><u>given</u><u> </u><u>equations</u><u>.</u>

I will choose to substitute in the first equation.

2x - 3y = 25 \\ 2(5) - 3y = 25 \\ 10 - 3y = 25 \\ 10 - 25 = 3y \\  - 1 5 = 3y \\ 3y  =  - 15 \\ y =  - 5

<u>Answer</u><u> </u><u>Check</u>

Substitute both x-value and y-value in any given equations

2x - 3y = 25 \\ 2(5) - 3( - 5) = 25 \\ 10 + 15 = 25 \\ 25 = 25

The equation is true. (<em>It</em><em> </em><em>is</em><em> </em><em>better</em><em> </em><em>to</em><em> </em><em>check</em><em> </em><em>both</em><em> </em><em>the</em><em> </em><em>answer</em><em> </em><em>for</em><em> </em><em>both</em><em> </em>equation.)

Thus the answer is (5,-5)

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In 1995, Hazel was 25 years older than her son Gary. In 2022, Hazel's age will be 150% of Gary's age. How old were they in 1995?
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so the rephrased question is
when hazel was x years old, she was 25 years older than son gary who was y old at that time (equation is x is 25 more than y or x=25+y)
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'of' in math means multiply so
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x=25+y
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subsitute 25+y for x in second euation
25+y+27=1.5(y+27)
add like terms
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I personally dislike decimals to multiply both sides by 2 to make 2 0.5's or 1 (you are technically supposed to distribute or divide both sides by 1.5) so
2y+104=3(y+27)
distribute
2y+104=3y+81
subtract 2y from both sides
104=y+81
subtract 81 from both sides
23=y
subsitute
x=25+y
x=25+23
x=48


Hazel was 48 and Gary was 23 in the year of 1995
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