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Given QR is congrent to LN and QR = 4x + 2 and LN = x + 7.
So, QR = LN
Hence, we can set up an equation as following:
4x + 2 = x + 7
4x + 2 - x = x + 7 - x Subtract x from each sides.
3x + 2 = 7 By simplifying.
3x + 2 - 2 = 7 - 2 Subtract 2 from each sides.
3x = 5
Divide each sides by 3 to isolate x.
So,
Next step is to plug in in QR = 4x+2 to get length of QR.
So,
Since 2 can be written as 2/1.
By multiplying the second fraction by the common denominator 3.
By simplifying the second fraction.
So,
Answer:
No solutions.
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
- Expanding
- Finding roots of a quadratic
- Standard Form: ax² + bx + c = 0
- Quadratic Formula:
Step-by-step explanation:
<u>Step 1: Define systems</u>
2x - y = 9
4x² + 3y² - 2x + y = 16
<u>Step 2: Rewrite systems</u>
2x - y = 9
- Subtract 2x on both sides: -y = 9 - 2x
- Divide -1 on both sides: y = 2x - 9
<u>Step 3: Redefine systems</u>
y = 2x - 9
4x² + 3y² - 2x + y = 16
<u>Step 4: Solve for </u><em><u>x</u></em>
<em>Substitution</em>
- Substitute in <em>y</em>: 4x² + 3(2x - 9)² - 2x + (2x - 9) = 16
- Expand: 4x² + 3(4x² - 36x + 81) - 2x + (2x - 9) = 16
- Distribute 3: 4x² + 12x² - 108x + 243 - 2x + 2x - 9 = 16
- Combine like terms: 16x² - 108x + 234 = 16
- Factor GCF: 2(8x² - 54x + 117) = 16
- Divide 2 on both sides: 8x² - 54x + 117 = 8
- Subtract 8 on both sides: 8x² - 54x + 109 = 0
- Define variables: a = 8, b = -54, c = 109
- Resubstitute:
- Exponents:
- Multiply:
- Subtract:
Here we see that we start to delve into imaginary roots. Since on a real number plane, we do not have imaginary roots, there would be no solution to the systems of equations.
<u>Step 5: Graph systems</u>
<em>We can verify our results.</em>
