solve the following pair of linear equations by the substitution method 3x/2-5y/3=-2. x/3+y/3=13/6
Answers
Explanation Step by Step:
Answer:
The value of x is 2 and y is 3.
Step-by-step explanation:
\frac{3 x}{2}-\frac{5 y}{3}=-2
2
3x
−
3
5y
=−2 ……………………..(1)
\frac{x}{3}+\frac{y}{2}=\frac{13}{6}
3
x
+
2
y
=
6
13
……………………….(2)
Consider equation \frac{3 x}{2}-\frac{5 y}{3}=-2
2
3x
−
3
5y
=−2
By taking LCM for the denominator 2 and 3 we get the LCM as 6
\begin{gathered}\begin{array}{l}{\frac{3 x}{2} \times \frac{6}{6}=\frac{9 x}{6}} \\ {\frac{5 y}{3} \times \frac{6}{6}=\frac{10 y}{6}} \\ {\frac{9 x}{6}-\frac{10 y}{6}=-2}\end{array}\end{gathered}
2
3x
×
6
6
=
6
9x
3
5y
×
6
6
=
6
10y
6
9x
−
6
10y
=−2
9x – 10y = -12 ……………………….. (3)
Consider equation 2
\frac{x}{3}+\frac{y}{2}=\frac{13}{6}
3
x
+
2
y
=
6
13
By taking LCM for the denominator 3 and 2 we get the LCM as 6
\begin{gathered}\begin{array}{l}{\frac{x}{3} \times \frac{6}{6}=\frac{2 x}{6}} \\ {\frac{y}{2} \times \frac{6}{6}=\frac{3 y}{6}} \\ {\frac{2 x}{6}+\frac{3 y}{6}=\frac{13}{6}}\end{array}\end{gathered}
3
x
×
6
6
=
6
2x
2
y
×
6
6
=
6
3y
6
2x
+
6
3y
=
6
13
2x + 3y = 13 …………………………(4)
By solving equation (3) and (4) we get
2x = 13-3y
x=13-3y/2 …………………………(5)
Put the value of x in eqn 3 we get
9[13-3y/2] – 10y =-12
117-27y-20y = -24 [By taking LCM and solving it]
117-47y=-24
-47y=-24-117
-47y=-141
Y=-141/-47
Y=3
Now put the value of y =3 in (5)
x=13-3(3)/2
x=13-9/2
x=4/2
x=2
Therefore we have x=2 and y=3
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