Question

what is the solution of the system of equations below?
$2x + 3y = 7$
$x + y = 3$
$(4, -1)$
$(4, 1)$
$(2, 1)$
$(1, 2)$
3 multiple choice 4 points
what is the solution of the system of equations shown in the graph below?
(0, -3) and (0, -1)
(-1, -2)
(-2, -1)
(1, 0) and (-3, 0)

Explanation:

Step1: Solve first system via substitution

From $x + y = 3$, get $y = 3 - x$.

Step2: Substitute into first equation

$2x + 3(3 - x) = 7$
$2x + 9 - 3x = 7$
$-x = 7 - 9$
$-x = -2$
$x = 2$

Step3: Find y for first system

$y = 3 - 2 = 1$

Step4: Identify graph intersection

The two lines cross at $(-1, -2)$.

Answer:

1. (2, 1)
2. (-1, -2)