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scoray [572]
3 years ago
7

What is the solution to the given system of equations? y=4x-3 y=-x-13

Mathematics
1 answer:
Paraphin [41]3 years ago
4 0
4x - 3 = -x - 13
4x + x = -13 + 3
5x = -10
x = -10/5
x = -2

y = 4x - 3
y = 4(-2) - 3
y = -8 - 3
y = -11

solution is (-2,-11)

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Find <img src="https://tex.z-dn.net/?f=a_%7B1%7D" id="TexFormula1" title="a_{1}" alt="a_{1}" align="absmiddle" class="latex-form
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Step-by-step explanation:

we are given

the sum,common difference and nth term of a geometric sequence

we want to figure out the first term

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\displaystyle S_{ \text{n}} =  \frac{ a_{1}(1 -  {r}^{n} )}{1 - r}

we are given that

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thus substitute:

\displaystyle 189=  \frac{ a_{1}(1 -  {( \frac{1}{2} )}^{3} )}{1 -  \frac{1}{2} }

to figure out a_1 we need to figure out the equation

simplify denominator:

\displaystyle  \frac{ a_{1}(1 -  {( \frac{1}{2} )}^{3} )}{ \dfrac{1}{2}  }  = 189

simplify square:

\displaystyle  \frac{ a_{1}(1 -  {( \frac{1}{8} )}^{} )}{ \dfrac{1}{2}  }  = 189

simplify substraction:

\displaystyle  \frac{ a_{1} (\frac{7}{8} )}{ \frac{1}{2}  }  = 189

simplify complex fraction:

\displaystyle   a_{1} (\frac{7}{8} ) \div { \frac{1}{2}  }  = 189

calculate reciprocal:

\displaystyle   a_{1} \frac{7}{8}   \times 2  = 189

reduce fraction:

\displaystyle   a_{1} \frac{7}{4}   \  = 189

multiply both sides by 4/7:

\displaystyle   a_{1} \frac{7}{4}  \times  \frac{4}{7}   \  = 189 \times  \frac{4}{7}

reduce fraction:

\displaystyle   a_{1}     = 27\times  4

simplify multiplication:

\displaystyle  a_{1}    = 108

hence,

\displaystyle  a_{1}    = 108

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