Question

graph the equations ( y = 3x - 12 ) and ( y = 4x + 3 ) using a graphing utility. choose the correct graph below.
a.

b.

c.

d.

all graphs are shown in (-24, 6) by (-80, 20) viewing windows with ( \text{xscl} = 2 ) and ( \text{yscl} = 5 ).
what is the solution to the system of equations? select the correct answer below and, if necessary, fill in any answer boxes to complete your choice.
a. the solution is ( x = square ), ( y = square ). (type integers or simplified fractions.)
b. the system of equations has infinitely many solutions.
c. the system of equations has no solution.

Explanation:

Step1: Set equations equal to each other

$3x - 12 = 4x + 3$

Step2: Solve for x

Subtract $3x$ from both sides: $-12 = x + 3$
Subtract 3 from both sides: $x = -15$

Step3: Find y using $y=3x-12$

$y = 3(-15) - 12 = -45 - 12 = -57$

Step4: Verify line properties

$y=3x-12$ has slope 3, y-intercept $(0,-12)$; $y=4x+3$ has slope 4, y-intercept $(0,3)$. The steeper line is $y=4x+3$, and they intersect at $(-15,-57)$, which matches graph A.

Answer:

Correct graph: A
Solution to the system:
A. The solution is $x = -15$, $y = -57$.