Solve each system by substitution.
1) y = 2x + 2
y = -5x + 16
2 answers:
Answer:
y = 6
x = 2
Step-by-step explanation:
rearrange the first equation in terms of x
x = (y - 2)/2
substiute x in the second equation
y = -5[(y-2)/2] +16
Now simpilify and solve for y
y = (-5y + 10)/2 +16
y = -5/2y + 5 + 16
y + 5/2y = 5 + 16
3.5y = 21
y = 6
Now substitue y in the first equation to solve for x
x = (6 - 2)/2
x = 2
Answer:
(2, 6)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtract Property of Equality
<u>Algebra I</u>
- Terms/Coefficients
- Solving systems of equations using substitution/elimination
Step-by-step explanation:
<u>Step 1: Define Systems</u>
y = 2x + 2
y = -5x + 16
<u>Step 2: Solve for </u><em><u>x</u></em>
<em>Substitution</em>
- Substitute in <em>y</em>: 2x + 2 = -5x + 16
- Add 5x on both sides: 7x + 2 = 16
- Subtract 2 on both sides: 7x = 14
- Divide 7 on both sides: x = 2
<u>Step 3: Solve for </u><em><u>y</u></em>
- Define equation: y = 2x + 2
- Substitute in <em>x</em>: y = 2(2) + 2
- Multiply: y = 4 + 2
- Add: y = 6
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