Question

Which ordered pair is the best estimate for the solution of the system of equations? y=−12x+4y=12x−3 (7, 1) (7, 0) (7, 0.5) (7.5, 0.5)

Answer 1

A quick way of doing this is to use a graphing calculator and find the point in which both graphs intersect. Another way of doing this is to substitute. Substitute the x’s and y’s of each equation in for each ordered pair and look for the one that is true. Though what’s confusing me is that, the solution is (0.3,0.5).

Answer 2

ANSWER

$(7,0.5)$

EXPLANATION

We want to solve the system;

$y = - \frac{1}{2} x + 4...(1)$
and

$y = \frac{1}{2} x - 3...(2)$

Add equations (1) and (2) to get,

$y + y = 4 + - 3$

This implies that,

$2y = 1$

$y = \frac{1}{2}$

or

$y = 0.5$

We put y=½ into equation (2) to get,

$\frac{1}{2} = \frac{1}{2} x - 3$
Multiply through by 2 to get,

$1 = x - 6$
This implies that,

$x = 1 + 6 = 7$

Therefore the best estimate for the system of equations is
$(7,0.5)$
The correct answer is C