solve the following system of linear equations using any algebric method. 2x+5y=3,x-3y=7.& 3y=11-2x,3x=y-11.

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flbyrne | (Level 3) Assistant Educator

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Solve the system of equations by substitution:

2x+5y=3   (1)

x-3y=7      (2)

Solve (2) for x.

x=7+3y     (3)

Substitute (3) in (1)

(2)(7+3y)+5y=3

14+6y+5y=3

11y=-11

y=-1

Substitute 1 for y in (3)

x=7+3(-1)

x=4

Verify by substituting 4 for x and -1 for y in (1)

(2)(4)+5(-1)=3

8-5=3

Thus x=4 and y=-1

Solve the second system of equation by elimination. Write the equations in standard form.

2x+3y=11    (1)

3x-y=-11      (2)

Multiply (2) by 3 and subtract from (1)

2x+3y=11

9x-3y=-33

------------

11x=-22

x=-2

Substitute -2 for x in (2)

(3)(-2)-y=-11

-6-y=-11

y=11-6=5

Verify by substituting -2 for x and 5 for y in (1)

2(-2)+3(5)=11

-4+15=11

Thus x=-2 and y=5

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