Question

Solve graphically: 4x+ 2y =6 & 2x-2y=6

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Answer 1

Answer:

First, we need to determine the x and y intercepts.

x-intercept

Set y equal to 0 and solve for x:

4x=(2⋅0)+6

4x=0+6

4x=6

4x4=64

4x4=32

x=32

(32,0)

x-intercept

Set x equal to 0 and solve for y:

4⋅0=2y+6

0=2y+6

0−6=2y+6−6

−6=2y+0

−6=2y

−62=2y2

−3=

Answer 2

$\large\underline{\sf{Solution-}}$

Consider first equation,

$\rm \: 4x + 2y = 6$

$\rm \: 2(2x + y) = 6$

$\rm \: 2x + y = 3$

Substituting 'x = 0' in the given equation, we get

$\rm \: 2 \times 0 + y = 3$

$\rm \: 0 + y = 3$

$\rm\implies \:y = 3$

Substituting 'y = 0' in the given equation, we get

$\rm \: 2x + 0 = 3$

$\rm \: 2x = 3$

$\rm\implies \:x = 1.5$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\color{blue}\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 3 \\ \\ \sf 1.5 & \sf 0 \end{array}} \\ \end{gathered}$

Consider second equation,

$\rm \: 2x - 2y = 6$

$\rm \: 2(x - y) = 6$

$\rm\implies \:x - y = 3$

Substituting 'x = 0' in the given equation, we get

$\rm \: 0 - y = 3$

$\rm \: - y = 3$

$\rm\implies \:y = - 3$

Substituting 'y = 0' in the given equation, we get

$\rm \: x - 0 = 3$

$\rm\implies \:x = 3$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\color{green}\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf - 3 \\ \\ \sf 3 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , 3), (1.5 , 0), (0, - 3) & (3 , 0)

➢ See the attachment graph.

So, from graph we concluded that given system of equations is consistent having unique solution and solution is

$\boxed{ \rm{ \: \: x \: = \: 2 \: \: \: and \: \: \: y \: = \: - \: 1 \: }}$