Math121 - Extra Problems Week 1-3

# Math121 - Extra Problems Week 1-3 - MATH 121 EXTRA PRACTICE...

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MATH 121 EXTRA PRACTICE PROBLEMS: WEEK 1-3 1) Verify that ( 8 3 , 5 3 ) is a solution to the system below. x + 11 y = 21 - 3 x - 6 y = - 18 2) Show that the following system of equations has no solutions. 1 10 x - 1 15 y = 1 3 x - 2 y = 14 3) Solve the system of equations below. 4 x + 7 y = - 19 - 6 x - 2 y = 3 4) Solve the system of equations below. 3 a - 4 b = 8 7 a - 5 b = - 3 5) Show that the following system of equations has an infinite number of solutions. Express the general solution in two different ways. - 24 x - 40 y = - 112 3 x + 5 y = 14 6) Suppose you are given that a line has slope m = 1 4 and a point on the line, (2 , 5) . (a) Find an equation for the line and express it in slope-intercept form. (b) At what point does this line in pt (a) intersect with the line 2 x + y = 7? (c) A line that is parallel to y = - 2 x + 7 passes through the point (3 , - 5).What is the equation of this line? (d) The equation we found in pt (c) also goes through the point (

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Unformatted text preview: x , 8). Determine the value of x . 7) Solve the following system of equations using Gaussian elimination. If there are no solutions, show why. 2 x + 5 y-3 z =-16-x-4 y + 2 z = 7 x + 6 y + 3 z = 17 8) Solve the following system of equations using Gaussian elimination. If there are no solutions, show why. 3 x-6 y-15 z =-3-5 x + 2 y + 4 z =-1 7 x-y-2 z = 5 1 2 MATH 121 EXTRA PRACTICE PROBLEMS: WEEK 1-3 9) Solve the following system of equations using Gaussian elimination. If there are no solutions, show why. 4 x + 6 y-4 z =-x + 8 y-3 z = 3-6 x-5 y + 5 z = 4 10) Solve the following system of equations using Gaussian elimination. If there are no solutions, show why. 2 x-7 y = 5 x + 10 z = 85 3 x + 4 y + 3 z = 29...
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