-x + 2y = 21 5x + 6y = 23
2 answers:
Answer:
(-5, 8)
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 equation by graphing
Step-by-step explanation:
<u>Step 1: Define systems</u>
-x + 2y = 21
5x + 6y = 23
<u>Step 2: Rewrite systems</u>
-x + 2y = 21
- Subtract 2y on both sides: -x = 21 - 2y
- Divide -1 on both sides: x = -21 + 2y
- Rearrange: x = 2y - 21
<u>Step 3: Redefine systems</u>
x = 2y - 21
5x + 6y = 23
<u>Step 4: Solve for </u><em><u>y</u></em>
<em>Substitution</em>
- Substitute in <em>x</em>: 5(2y - 21) + 6y = 23
- Distribute 5: 10y - 105 + 6y = 23
- Combine like terms: 16y - 105 = 23
- Add 105 on both sides: 16y = 128
- Divide 16 on both sides: y = 8
<u>Step 5: Solve for </u><em><u>x</u></em>
- Define original equation: 5x + 6y = 23
- Substitute in <em>y</em>: 5x + 6(8) = 23
- Multiply: 5x + 48 = 23
- Subtract 48 on both sides: 5x = -25
- Divide 5 on both sides: x = -5
<u>Step 6: Graph systems</u>
<em>Check the solution set.</em>
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Answer: h = 17
Step-by-step explanation: As a general rule, if an equation has any fractions in it, try to get rid of those fractions as soon as possible.
The quickest way to get rid of a fraction is to multiply both
sides of the equation by the denominator of the fraction.
So in this problem, we can get rid of the fraction in our
first step by multiplying both sides of the equation by 4.
On the left, the 4's cancel and on the right, 1(4) is 4.
Now we have h - 13 = 4.
Since 13 is being subtracted from <em>h</em>, to get <em>h</em> by itself,
we need to add 13 to both sides of the equation to get h = 17.
Now, we can check our answer by plugging 17 back
into the original equation shown below in italics.