Question

If $3x+5y=9$ and $5x+3y=7$ then what is the value of $x+y$?
$\left[4\right]$
[4 Marks]

Answer 1

Solution:
The given equations are,
3x + 5y = 9 ....(1)
5x + 3y = 7 ....(2)

Multiply equation (1) by 5 and equation (2) by 3, we get;
15x + 25y = 45 ...(3)
15x + 9y = 21 ...(4)
[1 Mark]

Subtracting (4) from (3)

15x + 25y = 45
15x + 9y = 21
$\underset{–}{---}$
16y = 24
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\therefore$ y = $\frac{24}{16}$ = $\frac{3}{2}$.
[1 Mark]

Putting y = $\frac{3}{2}$ in equation (1), we get

3x + 5$(\frac{3}{2})$ = 9
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\Rightarrow$ 3x + $\frac{15}{2}$ = 9
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\Rightarrow$ 3x = 9 - $\frac{15}{2}$
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\Rightarrow$ 3x = $\frac{3}{2}$
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\Rightarrow$ x = $\frac{1}{2}$
[1 Mark]

Thus, x + y = $\frac{3}{2}$ + $\frac{1}{2}$ = $\frac{3+1}{2}$ = $\frac{4}{2}$ = 2.
[1 Mark]