Question

1. $x - 3y = -4$

$2x - 6y = 6$

1. ella is a landscape photographer. she sells small prints for $50 each, and large prints for $75 each. one weekend at her gallery she sells a total of 52 prints for a total of $2,975. how many of each size print did ella sell?

Explanation:

Problem 8

Step1: Scale first equation

Multiply first equation by 2:
$$2(x - 3y) = 2(-4) \implies 2x - 6y = -8$$

Step2: Compare with second equation

Second equation: $2x - 6y = 6$
We have $-8 = 6$, which is false.

Step1: Define variables

Let $x$ = number of small prints, $y$ = number of large prints.
Set up system:
$$x + y = 52$$
$$50x + 75y = 2975$$

Step2: Isolate $x$ from first equation

$$x = 52 - y$$

Step3: Substitute into second equation

$$50(52 - y) + 75y = 2975$$
$$2600 - 50y + 75y = 2975$$
$$25y = 2975 - 2600$$
$$25y = 375$$

Step4: Solve for $y$

$$y = \frac{375}{25} = 15$$

Step5: Solve for $x$

$$x = 52 - 15 = 37$$

Answer:

There is no solution (the system is inconsistent).

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Problem 9