11.6 Exercise supplement

$\{\begin{array}{c}4x+y=5\\ -2x+3y=-13\end{array}$

$\{\begin{array}{c}-5x+2y=5\\ x+7y=-1\end{array}$

$\{\begin{array}{c}x-3y=17\\ 8x+2y=46\end{array}$

$\{\begin{array}{c}6m+5n=-9\\ 2m-4n=14\end{array}$

$\{\begin{array}{c}3x-9y=5\\ -x+3y=0\end{array}$

$\{\begin{array}{c}y=2x-5\\ 8x-75=5\end{array}$

$\{\begin{array}{c}x=8\\ 9y=5x-76\end{array}$

$\{\begin{array}{c}7x-2y=4\\ -14x+4y=-8\end{array}$

$\{\begin{array}{c}y=-x-7\\ x=y-5\end{array}$

$\{\begin{array}{c}20x+15y=-13\\ 5x-20y=13\end{array}$

$\{\begin{array}{c}x-6y=12\\ 4x+6y=18\end{array}$

$\{\begin{array}{c}8x+9y=0\\ 4x+3y=0\end{array}$

$\{\begin{array}{c}-5x+2y=1\\ 10x-4y=-2\end{array}$

$\{\begin{array}{c}2x-5y=3\\ 5x+2y=-7\end{array}$

$\{\begin{array}{c}6x+5y=14\\ 4x-8y=32\end{array}$

$\{\begin{array}{c}5x-7y=4\\ 10x-14y=1\end{array}$

$\{\begin{array}{c}2m+10n=0\\ -4m-20n=-6\end{array}$

$\{\begin{array}{c}7r-2s=6\\ -3r+5s=-15\end{array}$

$\{\begin{array}{c}28a-21b=-19\\ 21a+7b=15\end{array}$

$\{\begin{array}{c}72x-108y=21\\ 18x+36y=25\end{array}$

The sum of two numbers is 35. One number is 7 larger than the other. What are the numbers?

The difference of two numbers is 48. One number is three times larger than the other. What are the numbers?

A 35 pound mixture of two types of cardboard sells for $\$30.15$ . Type I cardboard sells for 90¢ a pound and type II cardboard sells for 75¢ a pound. How many pounds of each type of cardboard were used?

The cost of 34 calculators of two different types is $1139. Type I calculator sells for $35 each and type II sells for $32 each. How many of each type of calculators were used?

A chemistry student needs 46 ml of a 15% salt solution. She has two salt solutions, A and B, to mix together to form the needed 46 ml solution. Salt solution A is 12% salt and salt solution B is 20% salt. How much of each solution should be used?

A chemist needs 100 ml of a 78% acid solution. He has two acid solutions to mix together to form the needed 100-ml solution. One solution is 50% acid and the other solution is 90% acid. How much of each solution should be used?

One third the sum of two numbers is 12 and half the difference is 14. What are the numbers?

Two angles are said to be complementary if their measures add to 90°. If one angle measures 8 more than four times the measure of its complement, find the measure of each of the angles.

A chemist needs 4 liters of a 20% acid solution. She has two solutions to mix together to form the 20% solution. One solution is 30% acid and the other solution is 24% acid. Can the chemist form the needed 20% acid solution? If the chemist locates a 14% acid solution, how much would have to be mixed with the 24% acid solution to obtain the needed 20% solution?

A chemist needs 80 ml of a 56% salt solution. She has a bottle of 60% salt solution. How much pure water and how much of the 60% salt solution should be mixed to dilute the 60% salt solution to a 56% salt solution?