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Find the solution of the linear equation [tex]x + 2y = 8[/tex] that represents a point on the:

(i) [tex]x[/tex]-axis

(ii) [tex]y[/tex]-axis

Sagot :

GinnyAnsweridn
Certainly! Let's find the solutions for the linear equation [tex]\( x + 2y = 8 \)[/tex] considering the specific points on the axes.

### (i) Finding a point on the [tex]\( x \)[/tex]-axis

To determine a point on the [tex]\( x \)[/tex]-axis, we need to understand that any point on the [tex]\( x \)[/tex]-axis has a [tex]\( y \)[/tex]-coordinate of [tex]\( 0 \)[/tex]. Thus, we set [tex]\( y = 0 \)[/tex] in the equation and solve for [tex]\( x \)[/tex]:

[tex]\[ x + 2(0) = 8 \][/tex]

This simplifies to:

[tex]\[ x = 8 \][/tex]

So, the point that lies on the [tex]\( x \)[/tex]-axis is:

[tex]\[ (8, 0) \][/tex]

### (ii) Finding a point on the [tex]\( y \)[/tex]-axis

To determine a point on the [tex]\( y \)[/tex]-axis, we need to know that any point on the [tex]\( y \)[/tex]-axis has an [tex]\( x \)[/tex]-coordinate of [tex]\( 0 \)[/tex]. Thus, we set [tex]\( x = 0 \)[/tex] in the equation and solve for [tex]\( y \)[/tex]:

[tex]\[ 0 + 2y = 8 \][/tex]

This simplifies to:

[tex]\[ 2y = 8 \][/tex]

[tex]\[ y = \frac{8}{2} \][/tex]

[tex]\[ y = 4 \][/tex]

So, the point that lies on the [tex]\( y \)[/tex]-axis is:

[tex]\[ (0, 4) \][/tex]

### Summary

- The point on the [tex]\( x \)[/tex]-axis is [tex]\( (8, 0) \)[/tex].
- The point on the [tex]\( y \)[/tex]-axis is [tex]\( (0, 4) \)[/tex].
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