Question

10 multiple choice 2 points
solve:
3x - 2y = 2
6x - 4y = 5
(2/3, 0)
(7/6, 1/2)
no solution
none of these
11 multiple choice 2 points
what is the solution for x in the following system of equations?
-y = 2x - 3
y = -x + 1
4/3
2/3
2
4
12 multiple choice 2 points
the graph of the system of equations
{ x + 2y = 8
3x + 6y = 13
will give:
perpendicular lines
none of these
lines that coincide
parallel lines

Explanation:

Problem 10

Step1: Analyze equation scaling

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

Step2: Compare with second equation

Second equation: $6x - 4y = 5$
Contradiction ($4
eq 5$), so no solution.

Problem 11

Step1: Substitute $y$ into first equation

Substitute $y = -x + 1$ into $-y = 2x - 3$:
$-(-x + 1) = 2x - 3$

Step2: Simplify and solve for $x$

$x - 1 = 2x - 3$
$x - 2x = -3 + 1$
$-x = -2 \implies x = \frac{4}{3}$

Problem 12

Step1: Analyze equation scaling

Multiply first equation by 3:
$3(x + 2y) = 3(8) \implies 3x + 6y = 24$

Step2: Compare with second equation

Second equation: $3x + 6y = 13$
Same coefficients for $x,y$, different constants: lines are parallel.

Answer:

1. no solution
2. $\frac{4}{3}$
3. parallel lines