Question
Solve the following systems of equations graphically:
2x + 3y = 4
x - y + 3 = 0
✓
Answer
The given equations are,
2x + 3y = 4 ......(i)
x - y + 3 = 0 ........(ii)
Putting x = 0 in equation (i), we get,
⇒ 2 × 0 + 3y = 4
$\Rightarrow\text{y}=\frac{4}{3}$
$\Rightarrow\text{x}=0,\ \text{y}=\frac{4}{3}$
Putting y = 0 in equation (i), we get,
⇒ 2x + 3 × 0 = 4
⇒ x = 2
⇒ x = 2, y = 0
Use the following table to draw the graph.
Draw the graph by plotting the two points $\text{A}\Big(0, \frac{4}{3}\Big)$ and B(2, 0) from table.
Graph of the equation,
⇒ x - y = -3 ........(ii)
Putting x = 0 in equation (ii), we get,
⇒ 0 - y = -3
⇒ y = 3
⇒ x = 0, y = 3
Putting y = 0 in equation (ii), we get,
⇒ x - 0 = -3
⇒ x = -3
⇒ x = -3, y = 0
Use the following table to draw the graph.
Draw the graph by plotting the two points C(0, 3) and D(-3, 0) from table.
The two lines intersect at points P(-1, 2).
Hence, x = -1 and y = 2 is the solution.
2x + 3y = 4 ......(i)
x - y + 3 = 0 ........(ii)
Putting x = 0 in equation (i), we get,
⇒ 2 × 0 + 3y = 4
$\Rightarrow\text{y}=\frac{4}{3}$
$\Rightarrow\text{x}=0,\ \text{y}=\frac{4}{3}$
Putting y = 0 in equation (i), we get,
⇒ 2x + 3 × 0 = 4
⇒ x = 2
⇒ x = 2, y = 0
Use the following table to draw the graph.
|
X
|
0
|
2
|
|
Y
|
$\frac{4}{3}$
|
0
|
Graph of the equation,
⇒ x - y = -3 ........(ii)
Putting x = 0 in equation (ii), we get,
⇒ 0 - y = -3
⇒ y = 3
⇒ x = 0, y = 3
Putting y = 0 in equation (ii), we get,
⇒ x - 0 = -3
⇒ x = -3
⇒ x = -3, y = 0
Use the following table to draw the graph.
|
x
|
0
|
-3
|
|
y
|
3
|
0
|
The two lines intersect at points P(-1, 2).
Hence, x = -1 and y = 2 is the solution.
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