Lesson 15: Practice Problems

Problem 1

Solve: ${\begin{cases} y = 6 x \\ 4 x + y = 7 \end{cases}$

Problem 2

Solve: ${\begin{cases} y = 3 x \\ x = - 2 y + 70 \end{cases}$

Problem 3

Which equation, together with $y = - 1.5 x + 3$ , makes a system with one solution?

$y = - 1.5 x + 6$
$y = - 1.5 x$
$2 y = - 3 x + 6$
$2 y + 3 x = 6$
$y = - 2 x + 3$

Problem 4

The system $x - 6 y = 4$ , $3 x - 18 y = 4$ has no solution.

Change one constant or coefficient to make a new system with one solution.
Change one constant or coefficient to make a new system with an infinite number of solutions.

Problem 5

Match each graph to its equation.

Four graphs, A-D. A and B are positive slopes. C and D are negative slopes. Y-intercepts: A (0,3), B (0,-3) C (0,3) D (0,-3)

Graph A
Graph B
Graph C
Graph D

$y = 2 x + 3$
$y = - 2 x + 3$
$y = 2 x - 3$
$y = - 2 x - 3$

Problem 6

Here are two points: $(- 3, 4)$ , $(1, 7)$ . What is the slope of the line between them?

$\frac{4}{3}$
$\frac{3}{4}$
$\frac{1}{6}$
$\frac{2}{3}$