Answer:
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 - [tex]\frac{7}{2}[/tex]y = - 7
Then we sum both equations, eliminating x and isolating y to find its value!
y + (- [tex]\frac{7}{2}[/tex]y) = 3 + (- 7)
[tex]\frac{2}{2}[/tex]y + (- [tex]\frac{7}{2}[/tex]y) = - 4
Summing the fractions of y we have
- [tex]\frac{5}{2}[/tex] y = - 4 .: y = [tex]\frac{8}{5\\}[/tex] .: y = 1 [tex]\frac{3}{5}[/tex](we found y!)
Now we substitute y in one of the previous equations to find x:
-3x + 3 × ( [tex]\frac{8}{5\\}[/tex] ) = 9
-3x + [tex]\frac{24}{5\\}[/tex] = 9
-3x = 9 - [tex]\frac{24}{5}[/tex]
-3x = [tex]\frac{45}{5}[/tex] - [tex]\frac{24}{5}[/tex]
-3x = [tex]\frac{21}{5}[/tex]
x = [tex]\frac{21}{5}[/tex] ÷ -3 (this is tricky, but it's the same as [tex]\frac{21}{5}[/tex] × -[tex]\frac{1}{3}[/tex] )
x = - [tex]\frac{7}{5}[/tex] .: x = - 1 [tex]\frac{2}{5}[/tex](finally found x!)
Bringing everything together we have:
x = - 1 [tex]\frac{2}{5}[/tex]
y = 1 [tex]\frac{3}{5}[/tex]
I hope it helps :)
