draw the graphs representing the equations x+y=7& x-y=1 on the same graph paper. find the area of the triangles formed by these lines, the X-axis and the Y-axis
I'm not doing an exam but these are challenging questions and are for four marks pls do answer correctly with graph thanks
I'm not doing an exam but these are challenging questions and are for four marks pls do answer correctly with graph thanks
Answers & Comments
Verified answer
[tex]\large\underline{\sf{Solution-}}[/tex]
Consider, Ist line
[tex] \red{\bf \: x + y = 7} \\ \\ [/tex]
Substituting 'x = 0' in the given equation, we get
[tex]\rm \: 0 + y = 7 \\ [/tex]
[tex]\bf\implies \:y = 7 \\ \\ [/tex]
Substituting 'y = 0' in the given equation, we get
[tex]\rm \: x + 0 = 7 \\ [/tex]
[tex]\bf\implies \:x = 7 \\ \\ [/tex]
Hᴇɴᴄᴇ,
➢ Pair of points of the given equation are shown in the below table.
[tex] \red{\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 7 \\ \\ \sf 7 & \sf 0 \end{array}} \\ \end{gathered}} \\ [/tex]
Consider second line,
[tex] \red{\bf \: x - y = 1} \\ \\ [/tex]
Substituting 'x = 0' in the given equation, we get
[tex]\rm \: 0 - y = 1 \\ [/tex]
[tex]\bf\implies \:y \: = \: - \: 1 \\ \\ [/tex]
Substituting 'y = 0' in the given equation, we get
[tex]\rm \: x - 0 = 1 \\ [/tex]
[tex]\bf\implies \:x = 1 \\ \\ [/tex]
Hᴇɴᴄᴇ,
➢ Pair of points of the given equation are shown in the below table.
[tex] \red{\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf - 1 \\ \\ \sf 1 & \sf 0 \end{array}} \\ \end{gathered}} \\ [/tex]
➢ Now draw a graph using the points.
➢ See the attachment graph.
Now, Area of triangle formed by these lines with x - axis is
[tex]\rm \: Area_{ \triangle \: ADE \: } \\ [/tex]
[tex]\rm \: = \: \dfrac{1}{2} \times 6 \times 3 \\ [/tex]
[tex]\rm \: = \: 9 \: square \: units. \\ \\ [/tex]
Now, Area of triangle formed by these lines with y - axis is
[tex]\rm \: Area_{ \triangle \: BDC \: } \\ [/tex]
[tex]\rm \: = \: \dfrac{1}{2} \times 8 \times 4 \\ [/tex]
[tex]\rm \: = \: 16 \: square \: units. \\ \\ [/tex]
Answer:
: a place in which public records or historical materials (such as documents) are preserved an archive of historical manuscripts a film archive also : the material preserved —often used in plural reading through the archives. 2 : a repository or collection especially of information. archive. verb. archived; archiving.