Exam 4: Systems of Linear Equations

A croissant, a cup of coffee, and a fruit bowl from Kelley's Coffee Cart cost a total of $\$ 5.50$ , and a croissant costs twice as much as a cup of coffee. Kelley posts a notice announcing that, effective next week, the price of a croissant will go up $10 \%$ and the price of coffee will go up $10 \%$ . After the increase, the total price of the purchase will be $\$ 5.73$ . Find the cost of each item before the increase.

The largest angle of a triangle is 6 times the smallest angle and it is 3 times the other angle. Find the measure of the smallest angle.

By eating 1 cracker, 1 pretzel, and 1 cookie, one would ingest $149 \mathrm{mg}$ of sodium. By eating 8 pretzels and 8 cookies, one would ingest $936 \mathrm{mg}$ of sodium. By eating 6 crackers and 7 pretzels, one would ingest $535 \mathrm{mg}$ of sodium. How many $\mathrm{mg}$ of sodium are there in one pretzel?

Solve by any method. Assume $a$ and $b$ represent nonzero constants. - $7 \mathrm{ax}-2 \mathrm{y}=2$ $\mathrm{y}=5 \mathrm{ax}$

Solve the system of equations. If the system is inconsistent or has dependent equations, say so. - $x+4 y-z=3$ $-4 x-16 y+4 z=-12$ $3 \mathrm{x}+12 \mathrm{y}-3 \mathrm{z}=9$

How many liters (L) of a $40 \%$ alcohol solution must be mixed with $60 \mathrm{~L}$ of a $60 \%$ solution to get a $50 \%$ solution?

Without solving the following system of equations, tell what the solution is. Explain your answer. 5x-4y+6z =-3 -30x+24y-36z =18 20x-16y+24z =-12

Write the word or phrase that best completes each statement or answers the question -What is indicated by the occurrence of a true statement such as " $0=0$ " when you solve a system of two linear equation (in two variables) using elimination?

Tell how many solutions the system has. Do not actually solve. - $x-3=y$ $y+7=x$

The graphs below represent the supply and demand for a product at various prices per unit. At approximately what price does supply equal demand?

Solve the system by substitution or elimination. If a system is inconsistent or has dependent equations, say so. - $y=-\frac{15}{16} x$ $-5 x+4 y=7$

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $\frac{7}{3} x+\frac{5}{4} y=4$ $\frac{5}{6} x-2 y=21$

$x-y+5 z=4$ $5 x+z=0$ $\mathrm{x}+3 \mathrm{y}+\mathrm{z}=-12$

$3 x+3 y+z=1$ $4 x-5 y-z=-28$ $3 \mathrm{x}+\mathrm{y}+3 \mathrm{z}=-3$

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $y=-\frac{5}{6} x$ $5 x-6 y=-4$

Decide whether the ordered pair is a solution of the given system - $x+y=6$ $\mathrm{x}-\mathrm{y}=4 ;(5,1)$

In solving a system of three equations in three variables, it is impossible to eliminate two variables. Thus, the the final step yields the following equation: $\mathrm{z}=\mathrm{x}-4$ . How many solutions does this system have? Explain geometrically.

A company sells nuts in bulk quantities. When bought in bulk, peanuts sell for $\$ 1.20$ per pound, almonds for $\$ 2.55$ per pound, and cashews for $\$ 3.60$ per pound. Suppose a specialty shop wants a mixture of 280 pounds that will cost $\$ 2.89$ per pound. Find the number of pounds of each type of nut if the sum of the number of pounds of almonds and cashews is three times the number of pounds of peanuts. Round your answers to the nearest pound.

Solve the problem using a system of equations. -Paul invested four times as much money in an account paying $6 \%$ interest than he did in an account paying $1 \%$ interest. If the total interest paid was $\$ 1000$ , how much did he invest in each?

The perimeter of a rectangle is $28 \mathrm{~cm}$ . The length is $8 \mathrm{~cm}$ longer than the width. What are the length and width of the rectangle?