What is the value of \( x \) in the following system of equations?

\[
15x - 12y = 13
\]

\[
30x + 9y = 4
\]

{ 30 x + 9 y = 4 15 x − 12 y = 13 ∣ m u lt i pl y b y − 2 ​ { 30 x + 9 y = 4 − 30 x + 24 y = − 26 ​ a dd i t i o n m e t h o d 33 y = − 22 ∣ d i v i d e b y 33 y = − 33 22 ​ 15 x = 13 + 12 y x = 15 13 + 12 y ​ = 15 13 + 12 ∗ ( − 33 22 ​ ) ​ = 15 13 − 33 264 ​ ​ = 15 13 − 8 ​ = 3 1 ​ S o l u t i o n i s x = 3 1 ​ .

Answered by luana | 2024-06-10

so assuming that x and y are the same value in both equations we can make the first equation negative (multiply the whole thing by -1) and get
-15x+12y=-13 we multiply it by 2 and get -30x+24y=-26 we add this to the second equation (30x+9y=4)+(-30x+24y=-26) 30x-30x+24y+9y=-22 or 33y=-22 divide both sides by 11 3y=-2 divide both sides by 3 y=-2/3
we subtitute it into the first equation 15x-12(-2/3)=13 15x-(-24/3)=13 15x+8=13 subtract 8 from both sides 15x=5 divide both sides by 5 3x=1 divide both sides by 3 x=1/3
so x=1/3 y=-2/3

Answered by apologiabiology | 2024-06-10

To solve the system of equations 15x - 12y = 13 and 30x + 9y = 4, we first eliminate one of the variables and find that y = -2/3. Substituting back gives us the final value of x = 1/3.
;

Answered by luana | 2024-10-31