Mathematics: Estimate the solution to the system of Equations

Estimate the solution to the system of Equations

allhailkingmilkdud

24.01.2022

Answer letter D

Step-by-step explanation:

-3x + 3y = 9

2x - 7y = -14

Let's start by simplifying both equations:

-3x + 3y = 9 (divide everything by 3)

2x - 7y = -14 (divide everything by 2)

We will then have:

-x + y = 3

x - $\frac{7}{2}$ y = - 7

Then we sum both equations, eliminating x and isolating y to find its value!

y + (- $\frac{7}{2}$ y) = 3 + (- 7)

$\frac{2}{2}$ y + (- $\frac{7}{2}$ y) = - 4

Summing the fractions of y we have

- $\frac{5}{2}$ y = - 4 .: y = $\frac{8}{5\\}$ .: y = 1 $\frac{3}{5}$ (we found y!)

Now we substitute y in one of the previous equations to find x:

-3x + 3 × ( $\frac{8}{5\\}$ ) = 9

-3x + $\frac{24}{5\\}$ = 9

-3x = 9 - $\frac{24}{5}$

-3x = $\frac{45}{5}$ - $\frac{24}{5}$

-3x = $\frac{21}{5}$

x = $\frac{21}{5}$ ÷ -3 (this is tricky, but it's the same as $\frac{21}{5}$ × - $\frac{1}{3}$ )

x = - $\frac{7}{5}$ .: x = - 1 $\frac{2}{5}$ (finally found x!)

Bringing everything together we have:

x = - 1 $\frac{2}{5}$

y = 1 $\frac{3}{5}$

I hope it helps :)

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