# 9.6.3. Solving Two Equations in Two Variables, One Is of the First Degree, and the Other Is of the Second Degree

Determine the solution set of the two equations and rounding the result to the nearest two decimal places if needed.

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Determine the dimensions of a rectangle having a perimeter of cm and an area of .

• Acm, cm
• Bcm, cm
• Ccm, cm
• Dcm, cm
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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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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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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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Find the solution set of the two equations and .

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The length of a rectangle is cm more than its width. Given that its area is , determine its perimeter.

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Find the two points lying on the straight line , where the -coordinate is twice the square of its -coordinate, rounding the result to the nearest two decimal places.

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Find a solution of the two equations and .

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Find the solution set of the two equations and .

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Find in the solution set of the following pair of equations: and .

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If and , find .

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A right triangle has a hypotenuse length of cm and a perimeter of cm. Find the lengths of the other two sides.

• Acm, cm
• Bcm, cm
• Ccm, cm
• Dcm, cm
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Find the solution set of the two equations and .

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A car driver moved a distance of km towards the west, then a distance of km towards the south. If the sum of the two distances is km, and the distance between the starting point and the end point is 35 km, find the distance which the driver moved west and that he moved south.

• Akm, km
• Bkm, km
• Ckm, km
• Dkm, km
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Determine the solution set of the pair of equations and .

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The age of a father exceeds 2 times the age of his son by 14 years, and the sum of the squares of their ages exceeds 4 times the product of their ages by 4. Find their ages.

• A the father's age years, the son's age years
• B the father's age years, the son's age years
• C the father's age years, the son's age years
• D the father's age years, the son's age years
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The difference between the perimeters of two square-shaped pieces of land is 12 metres and that between their areas is 45 square metres. Find the side length of each of them.

• A6 metres, 9 metres
• B12 metres, 15 metres
• C9 metres, 12 metres
• D18 metres, 21 metres
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In a right-angled triangle, the length of one of the two sides between which the right angle lies is cm less than that of the other, and the hypotenuse is cm long. Find the perimeter to the nearest centimetre.

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The length of a rectangle is cm, its width is cm, and its area is . If its length decreased by cm and its width increased by cm, it will become a square. Find the area of the square.

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In a two-digit number, the units digit is times times the tens digit. Determine the original number, given that the product of the two digits is of its value.

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If the ratio between the perimeters of two squares is , find the ratio between their areas.

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Determine the increase in the area of a square when its side length is increased by cm, given that its side length is cm.

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Find the two positive numbers whose difference is 1, and the sum of their squares is 113.

• A9, 8
• B11, 10
• C8, 7
• D10, 9
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The equation is of the degree.

• Azeroth
• Bfirst
• Csecond
• Dthird
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Find the two numbers that one of which is the additive inverse of the other, and the sum of their squares is 72.

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