Solving a System of Linear Equations via Elimination

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When substitution, is not warranted because you cannot easily solve one of the equations for one of the variables entirely in terms of the other variable, and then elimination may be considered. Solving a system using linear elimination involves multiplying each equation by conveniently selected differing constants so that a variable will be eliminated when the equations are added or subtracted. Once a variable is eliminated, we solve for the remaining variable.

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Consider the following system of linear equations. The first equation is given as 4x - 5y = -2 and the second is 5x + 5y = 20. What would be the first step in solving this system using elimination? Choose the best answer. *

1 point

Eliminate the x by multiplying the first equation by 5 and the second by -4 then adding the equations.

Eliminate the y simply by adding the two equations because the -5y and the 5y will add to zero.

Eliminate the y by multiplying both equations by 5 then adding the equations; -25y and 25y will add to zero.

Eliminate the x by multiplying the first equation by 5 and the second by 4 then subtracting the second equation from the first.

Consider the same system of linear equations. The first equation is given as 4x - 5y = -2 and the second is 5x + 5y = 20. The point of intersection is? *

1 point

(12, 10)

(3, 1)

(2, 2)

Consider the following system of linear equations. The first equation is given as 6x + y = 3 and the second is 14x - 7y = 7. What is the point of intersection of the two lines described? *

1 point

(0, 3)

(0, -1)

(1/2, 0)

Consider the following system of linear equations. The first equation is given as 3x - 4y = -9 and the second is 18x - 5y = 3. What is the point of intersection of the two lines described? *

1 point

(5, -6)

(1, 3)

(6, 21)

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