Question

Solve the equations graphically: $7x+8y=64$ and $x+4y=12$

• A. $(8,1)$
• B. $(-8,-1)$
• C. $(-8,1)$
• D. $(8,-1)$

Answer 1

Answer: (A)

$(8,1)$

$7x+8y=64$ ----- (1)
$x+4y=12$ ----- (2)
From equation (1) assume the value of $x$ and $y$ to satisfy the equation to zero.
$7x+8y-64=0$ ------ (3)
Put $x=0,y=8$ in equation (3)
$7\left(0\right)+8\left(8\right)-64=0$
$0+64-64=0$
$0=0$
Again put $x=8,y=1$ in equation (3)
$7\left(8\right)+8\left(1\right)-64=0$
$56+8-64=0$
$0=0$
Now plotting $(0,8),(8,1)$ and joining them, we get a straight line.
From equation (2) assume the value of $x$ and $y$ to satisfy the equation to zero.
$x+4y-12=0$ ----- (4)
Put $x=0,y=3$ in equation (4)
$0+4\left(3\right)-12=0$
$12-12=0$
$0=0$
Again put $x=8,y=1$ in equation (4)
$8+4\left(1\right)-12=0$
$8+4-12=0$
$0=0$
Plotting $(0,3),(8,1)$ and joining them, we get another straight line.
These lines intersect at the point $(8,1)$ and therefore the solution of the equation is $x=8,y=1$