Question 269017: Can u please help me solve this equation by subsitution or the elimination method:
2x-3y=-21
5x+6y=4 Found 2 solutions by persian52, checkley77:Answer by persian52(161) (Show Source):
You can put this solution on YOUR website! Here's in detail how to solve the equation by using substitution method, hope you get it now!
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►► 2x-3y=-21_5x+6y=4
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►Since -3y does not contain the variable to solve for, move it to the right-hand side of the equation by adding 3y to both sides.
2x=3y-21_5x+6y=4
►Divide each term in the equation by 2.
(2x)/(2)=(3y)/(2)-(21)/(2)_5x+6y=4
►Simplify the left-hand side of the equation by canceling the common terms.
x=(3y)/(2)-(21)/(2)_5x+6y=4
►Simplify the right-hand side of the equation by simplifying each term.
x=(3(y-7))/(2)_5x+6y=4
►Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is (3(y-7))/(2).
x=(3(y-7))/(2)_5((3(y-7))/(2))+6y=4
►Multiply 3 by each term inside the parentheses.
x=((3y-21))/(2)_5((3(y-7))/(2))+6y=4
►Remove the parentheses around the expression 3y-21.
x=(3y-21)/(2)_5((3(y-7))/(2))+6y=4
►Divide each term in the numerator by the denominator.
x=(3y)/(2)-(21)/(2)_5((3(y-7))/(2))+6y=4
►Multiply 3 by each term inside the parentheses.
x=(3y)/(2)-(21)/(2)_5(((3y-21))/(2))+6y=4
►Remove the parentheses around the expression 3y-21.
x=(3y)/(2)-(21)/(2)_5((3y-21)/(2))+6y=4
►Divide each term in the numerator by the denominator.
x=(3y)/(2)-(21)/(2)_5((3y)/(2)-(21)/(2))+6y=4
►Combine the numerators of all expressions that have common denominators.
x=(3y)/(2)-(21)/(2)_5((3y-21)/(2))+6y=4
►Multiply 5 by each term inside the parentheses.
x=(3y)/(2)-(21)/(2)_(15(y-7))/(2)+6y=4
►Multiply 15 by each term inside the parentheses.
x=(3y)/(2)-(21)/(2)_((15y-105))/(2)+6y=4
►Remove the parentheses around the expression 15y-105.
x=(3y)/(2)-(21)/(2)_(15y-105)/(2)+6y=4
►Divide each term in the numerator by the denominator.
x=(3y)/(2)-(21)/(2)_(15y)/(2)-(105)/(2)+6y=4
►Combine the numerators of all expressions that have common denominators.
x=(3y)/(2)-(21)/(2)_(15y-105)/(2)+6y=4
►Factor out the GCF of 15 from each term in the polynomial.
x=(3y)/(2)-(21)/(2)_(15(y)+15(-7))/(2)+6y=4
►Factor out the GCF of 15 from 15y-105.
x=(3y)/(2)-(21)/(2)_(15(y-7))/(2)+6y=4
►Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of 2.
x=(3y)/(2)-(21)/(2)_(15(y-7))/(2)+6y*(2)/(2)=4
►Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 2.
x=(3y)/(2)-(21)/(2)_(15(y-7))/(2)+(6y*2)/(2)=4
►Multiply 6y by 2 to get 12y.
x=(3y)/(2)-(21)/(2)_(15(y-7))/(2)+(12y)/(2)=4
►The numerators of expressions that have equal denominators can be combined. In this case, (15(y-7))/(2) and ((12y))/(2) have the same denominator of 2, so the numerators can be combined.
x=(3y)/(2)-(21)/(2)_(15(y-7)+(12y))/(2)=4
►Simplify the numerator of the expression.
x=(3y)/(2)-(21)/(2)_(27y-105)/(2)=4
►Factor out the GCF of 3 from each term in the polynomial.
x=(3y)/(2)-(21)/(2)_(3(9y)+3(-35))/(2)=4
►Factor out the GCF of 3 from 27y-105.
x=(3y)/(2)-(21)/(2)_(3(9y-35))/(2)=4
►Multiply each term in the equation by 2.
x=(3y)/(2)-(21)/(2)_(3(9y-35))/(2)*2=4*2
►Simplify the left-hand side of the equation by canceling the common terms.
x=(3y)/(2)-(21)/(2)_3(9y-35)=4*2
►Multiply 4 by 2 to get 8.
x=(3y)/(2)-(21)/(2)_3(9y-35)=8
►Divide each term in the equation by 3.
x=(3y)/(2)-(21)/(2)_(3(9y-35))/(3)=(8)/(3)
►Simplify the left-hand side of the equation by canceling the common terms.
x=(3y)/(2)-(21)/(2)_9y-35=(8)/(3)
►Since -35 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 35 to both sides.
x=(3y)/(2)-(21)/(2)_9y=35+(8)/(3)
►Simplify the right-hand side of the equation.
x=(3y)/(2)-(21)/(2)_9y=(113)/(3)
►Divide each term in the equation by 9.
x=(3y)/(2)-(21)/(2)_(9y)/(9)=(113)/(3)*(1)/(9)
►Simplify the left-hand side of the equation by canceling the common terms.
x=(3y)/(2)-(21)/(2)_y=(113)/(3)*(1)/(9)
►Simplify the right-hand side of the equation by simplifying each term.
=► x=(3y)/(2)-(21)/(2)_y=(113)/(27)
You can put this solution on YOUR website! 2x-3y=-21 multiply by 2 & add.
5x+6y=4
4x-6y=-42
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9x=-38
x=-38/9 ans.
2*-38/9-3y=-21
-76/9-3y=-21
-3y=-21+76/9
-3y=-189/9+76/9
-3y=-113/9
y=(-113/9)/-3
y=-113/9*1/-3
y=-113/-27
y=113/27 ans.
Proof:
5*-38/9+6*113/27=4
-190/9+678/27=4
-570/27+678/27=4
108/27=4
4=4
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