Answer:
(-1, 1)
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
- Equality Properties
<u>Algebra I</u>
- Solving systems of equations using substitution/elimination
- Solving systems of equations by graphing
Step-by-step explanation:
<u>Step 1: Define systems</u>
3 + 2x - y = 0
-3 - 7y = 10x
<u>Step 2: Rewrite systems</u>
3 + 2x - y = 0
- Add <em>y</em> to both sides: 3 + 2x = y
<u>Step 3: Redefine systems</u>
y = 2x + 3
-3 - 7y = 10x
<u>Step 4: Solve for </u><em><u>x</u></em>
<em>Substitution</em>
- Substitute in <em>y</em>: -3 - 7(2x + 3) = 10x
- Distribute -7: -3 - 14x - 21 = 10x
- Combine like terms: -14x - 24 = 10x
- Add 14x on both sides: -24 = 24x
- Divide 24 on both sides: -1 = x
- Rewrite: x = -1
<u>Step 5: Solve for </u><em><u>y</u></em>
- Define original equation: -3 - 7y = 10x
- Substitute in <em>x</em>: -3 - 7y = 10(-1)
- Multiply: -3 - 7y = -10
- Add 3 to both sides: -7y = -7
- Divide -7 on both sides: y = 1
<u>Step 6: Graph</u>
<em>Check the solution set.</em>
Answer:
Step-by-step explanation:
a) Here we have:
"In Family A, the youngest child is 7 years younger than the oldest, who is 18"
Let's define:
Y = age of the youngest child.
O = age of the oldest child.
Then we know that:
Y = O - 7
O = 18
Then we can replace the second equation into the first one:
Y = 18 - 7 = 11.
b) Here we have:
"In Family B, the middle child is 5 years older than the youngest child."
Let's define:
Y = age of the youngest child.
M = age of the middle child.
Here we have only one equation:
M = Y + 5.
10 minutes : 8 problems
x minutes : 60 problems
10 * 60/8 = 150/2 = 75 minutes for 60 problems
The ratio of the surface areas of similar solids is equal to the square of their scale factor and that the ratio of their volumes is equal to the cube of their scale factor.
Answer:
x=6
Step-by-step explanation:
ln 1=0
x-5=1
x=6