# 9.6.1. Solving Two First-Degree Equations Algebraically and Geometrically

Find the intersection point of the two straight lines and .

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Find the solution set of and .

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If is a solution of the equation , find .

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The straight line intersects the -axis at the point .

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Find the solution set of the two equations and .

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If is the solution of the two equations and , find and .

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Find the solution set of and together.

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The two straight lines and are .

• Aperpendicular
• Bintersecting
• Cparallel
• Dcoincident
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The difference between the measures of two acute angles in a right triangle is . Find the measure of both angles.

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If there are infinite numbers of solutions for the two equations and , find .

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If there is only one solution for the two equations and , then cannot equal .

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Find the solution set of the two equations and .

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13 teams are participating in the African cup of Nations and the number of non-Arab teams is 5 teams more than three times the Arab teams. Find the number of the Arab teams participating in the championship.

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If , , and , find and .

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The sum of the ages of Dalia and Yasser is 66. Given that 2 years from now the difference between their ages will be 4 years, determine their ages 9 years from now.

• A44, 31
• B35, 31
• C26, 22
• D44, 40
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A rectangle has a length that is cm more than its width. If the perimeter of the rectangle is cm, find its area.

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Determine where the two straight lines and intersect.

• Corigin
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Find the solution set of the two equations and .

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Find the solution set of the two equations and .

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If and , determine .

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Determine the value of which makes the two straight lines and parallel.

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If the equation of straight line is > and equation of the straight line is , where , origin point, and , find the surface area of the triangle .

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If , find .

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If and are two solutions of the equation , find the values of and .

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Given that and , determine the values of and .

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If exceeds double by 14, then .

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Determine the two natural numbers whose sum is 69 and difference is 3.

• A72, 33
• B36, 33
• C45, 33
• D15, 54
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If the current ages of two people are and , then the sum of their ages 7 years ago was years.

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Given that the difference between two numbers is 11, and when twice the greater number is added to 6 times the smaller one it becomes 38, determine the two numbers.

• A13, 24
• B26, 15
• C5, 16
• D13, 2
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The cost of 2 pens and 2 books is LE. If the number of pens increases by 2 and the number of books decreases by 1, the cost becomes LE. Find the cost of one pen and that of one book.

• A a book LE, a pen LE
• B a book LE, a pen LE
• C a book LE, a pen LE
• D a book LE, a pen LE
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Determine the rational number that becomes if 1 is subtracted from its numerator and denominator, and it becomes if 7 is added to its denominator.

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Determine the two-digit number whose sum of digits is 9, and when the two digits are reversed, the resulting number is more than the original one by 27.

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Given that the measures of the two base angles of an isosceles triangle are and , and the measure of the vertex angle is , find the values of and .

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The weight of 7 apples and 12 bananas is gm, and that of 12 apples and 10 bananas is gm. Determine the weight of 4 apples and 9 bananas, given that they are identical.

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If a sum of LE is to be changed into 44 banknotes which have the values of piastres and piastres, find the number of the banknotes needed from each type.

• A36 of piastres, 8 of piastres
• B136 of piastres, 156 of piastres
• C156 of piastres, 136 of piastres
• D8 of piastres, 36 of piastres
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The sum of ages of a man and his son is 57 years. If the man's age exceeds 2 times his son's age by 9 years, find the age of each of them.

• A22 years, 41 years
• B16 years, 41 years
• C22 years, 70 years
• D16 years, 35 years
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A man's age was four times his daughter's age four years ago, and his age will be three times the age of his daughter’s five years later. Find the age of each of them now.

• A22 years, 76 years
• B8 years, 76 years
• C8 years, 72 years
• D22 years, years
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Find the side length of the equilateral triangle below.

• Acm
• Bcm
• Ccm
• Dcm
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Given that , determine the value of .

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If and , determine .

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Given that and , determine the value of .

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Determine the solution set of the pair of equations and .

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Find the solution set of and .

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