Question
Determine, graphically whether the system of equation $x - 2y = 2, 4x - 2y = 5$ is consistent or in-consistent.
✓
Answer
We have
$x - 2y = 2$
$4x - 2y = 5$
Now$ x - 2y = 2$
$⇒ x = 2 + 2y$
When $y = 0$, we have,
$x = 2 + 2 × 0 = 2$
when $y = -1$, we have,
$x = 2 + 2 × (-1) = 0$
Thus, we have the following table giving points on the line $x - 2y = 2$
Now, $4x - 2y = 5$
$⇒ 4x = 5 + 2y$
$\Rightarrow\text{x}=\frac{5+2\text{y}}{4}$
When $y = 0$, we have
$\text{x}=\frac{5+2\times0}{4}=\frac{5}{4}$
When $y = 1$, we have
$\text{x}=\frac{5+2\times1}{4}=\frac{7}{4}$
Thus, we have the following table giving points on the line $4x - 2y = 5$
Graph of the given equations,
Clearly, the two lines intersect at $(i!).$
Hence, the system of equations is consistent.
$x - 2y = 2$
$4x - 2y = 5$
Now$ x - 2y = 2$
$⇒ x = 2 + 2y$
When $y = 0$, we have,
$x = 2 + 2 × 0 = 2$
when $y = -1$, we have,
$x = 2 + 2 × (-1) = 0$
Thus, we have the following table giving points on the line $x - 2y = 2$
|
$x$
|
$2$
|
$0$
|
|
$y$
|
$0$
|
$-1$
|
$⇒ 4x = 5 + 2y$
$\Rightarrow\text{x}=\frac{5+2\text{y}}{4}$
When $y = 0$, we have
$\text{x}=\frac{5+2\times0}{4}=\frac{5}{4}$
When $y = 1$, we have
$\text{x}=\frac{5+2\times1}{4}=\frac{7}{4}$
Thus, we have the following table giving points on the line $4x - 2y = 5$
| $x$ | $\frac{5}{4}$ | $\frac{7}{4}$ |
| $y$ | $0$ | $1$ |
Clearly, the two lines intersect at $(i!).$
Hence, the system of equations is consistent.
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