Question

CLASS 10
SUBJECT: MATHEMATICS
TOPIC LINEAR EQUATIONS IN TWO VARIABLES
1. Solve graphically the system of linear equations: X+3y = 11, 3x+2y=12​

Answer 1

$\bf{\underline{\underline{\sf{Given:}}}}$

Equation 1 → $\red{\tt{x+3y = 11}}$

Equation 2 → $\blue{\tt{3x+2y=12}}$

$\star \green{\sf{Solving\:\:the\:\:given\:\:equations\:\:graphically.}}$

Now,

Equation 1 → $\red{\tt{x+3y = 11}}$

$\boxed{\begin{array}{| c | c | c | c |}\cline{1-4} \bf x & 2 & 5 &8\\ \cline{1-4} \bf y & 3 & 2 &1\\ \cline{1-4} \end{array}}$

We get the points. (Taking some value of x and finding y.)

Point = $\red{\tt{(2,3)}}$ ;  $\red{\tt{(5,2)}}$ ;  $\red{\tt{(8,1)}}$  

$\rule{200}2$

Equation 2 → $\blue{\tt{3x+2y=12}}$

$\boxed{\begin{array}{| c | c | c | c |}\cline{1-4} \bf x & 0 & 1 &2\\ \cline{1-4} \bf y & 6 & 4.5 &3\\ \cline{1-4} \end{array}}$

We get the points. (Taking some value of x and finding y.)

Point = $\blue{\tt{(0,6)}}$ ;  $\blue{\tt{(1,4.5)}}$ ;  $\blue{\tt{(2,3)}}$  

Now,

Plotting the points in the graph.

$\star \pink{\underline{\sf{GRAPH\:\:IS\:\:IN\:\:THE\:\:ATTACHED\:\:IMAGE}}}$

$\rule{200}2$

Observation:

• The equations has intersecting lines.
• (2,3) is the intersecting point.
• Number of solution = exactly one solution.