Chapter 2.4A, Problem 1MCQ

To determine

To solve: the system of equations with the help of graphing.

Answer to Problem 1MCQ

  $\left(4,3\right)$

Explanation of Solution

Given information:

  $\frac{1}{2}x+5y=17$… (1)

  $3x+2y=18$… (2)

Calculation:

Make table for equation (1) and (2) as shown below.

$\frac{1}{2}x+5y=17$		$3x+2y=18$
$x$	$y$	$x$	$y$
0	$\raisebox{1ex}{$17$}\!\left/ \!\raisebox{-1ex}{$5$}\right.$	0	9
34	0	6	0
2	$\raisebox{1ex}{$16$}\!\left/ \!\raisebox{-1ex}{$5$}\right.$	2	6
4	3	4	3
$-2$	$\raisebox{1ex}{$18$}\!\left/ \!\raisebox{-1ex}{$5$}\right.$	$-2$	12

Now, plot these points on the graph as shown below. The equation (1) and (2) are denoted by red and blue lines respectively.

  

Since the two lines intersect at $\left(4,3\right)$ . Thus, the solution for the system of equations is $\left(4,3\right)$ .