7.4 Review

Consider the system of equations below:
$3x - y = 7$
$x - 2y = 4$

a) Is the ordered pair (2, –1) a solution?

b) Is the ordered pair (–2, –3) a solution?
Solve the given systems by graphing. State how many solutions each system has. Check your answers using your graphing calculator.

a) $-x + y = 1$
$3x + 2y = 12$ b) $y = 3x - 1$
$6x - 2y = 12$ c) $2x + 4y = 8$
$x + 2y = 4$
Alisha is making an 18-ounce coffee beverage that is made from brewed coffee and milk. The number of ounces of brewed coffee is 5 times greater than the number of ounces of milk. The following system of equations can be used to represent the scenario:
$y = 5x$
$y + x = 18$

How many ounces of coffee and how many ounces of milk does Alisha need? Use the grid below to find the answer. Check your answer using your graphing calculator.
Solve the systems by substitution.

a)

$y = -2x + 2$
$2x + 5y = -14$

b)

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

c)

$3x + y = 1$
$-4x + y = 15$

d)

$x + 2y = -1$
$2x + 3y = 1$

e)

$y = -2x - 1$
$y = -\dfrac{1}{3}x + 4$

f)

$15x + 2y = 6$
$-5x + 2y = -4$
Solve the systems by elimination.

a)

$2x + 3y = 12$
$4x - 3y = 6$

b)

$3x + 2y = 16$
$x - y = 2$

c)

$4x - y = 15$
$2x + y = 9$

d)

$2x - 5y = 7$
$3x - y = 17$

e)

$7x + y = -4$
$13x + 3y = 4$

f)

$3x - 5y = -9$
$5x + 2y = 16$