|
Question 389005: 5r - 9s = -37
9r + 5s = 103
solve using elimination method
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! 5r-9s=-37,9r+5s=103
Since -9s does not contain the variable to solve for, move it to the right-hand side of the equation by adding 9s to both sides.
5r=9s-37_9r+5s=103
Divide each term in the equation by 5.
(5r)/(5)=(9s)/(5)-(37)/(5)_9r+5s=103
Simplify the left-hand side of the equation by canceling the common factors.
r=(9s)/(5)-(37)/(5)_9r+5s=103
Combine the numerators of all expressions that have common denominators.
r=(9s-37)/(5)_9r+5s=103
Replace all occurrences of r with the solution found by solving the last equation for r. In this case, the value substituted is ((9s-37))/(5).
r=(9s-37)/(5)_9((9s-37)/(5))+5s=103
Remove the parentheses around the expression 9s-37.
r=(9s-37)/(5)_9((9s-37)/(5))+5s=103
Divide each term in the numerator by the denominator.
r=(9s)/(5)-(37)/(5)_9((9s-37)/(5))+5s=103
Remove the parentheses around the expression 9s-37.
r=(9s)/(5)-(37)/(5)_9((9s-37)/(5))+5s=103
Divide each term in the numerator by the denominator.
r=(9s)/(5)-(37)/(5)_9((9s)/(5)-(37)/(5))+5s=103
Combine the numerators of all expressions that have common denominators.
r=(9s)/(5)-(37)/(5)_9((9s-37)/(5))+5s=103
Divide each term in the numerator by the denominator.
r=(9s)/(5)-(37)/(5)_9((9s)/(5)-(37)/(5))+5s=103
Multiply 9 by each term inside the parentheses.
r=(9s)/(5)-(37)/(5)_(81s-333)/(5)+5s=103
Divide each term in the numerator by the denominator.
r=(9s)/(5)-(37)/(5)_(81s)/(5)-(333)/(5)+5s=103
Combine the numerators of all expressions that have common denominators.
r=(9s)/(5)-(37)/(5)_(81s-333)/(5)+5s=103
Factor out the GCF of 9 from each term in the polynomial.
r=(9s)/(5)-(37)/(5)_(9(9s)+9(-37))/(5)+5s=103
Factor out the GCF of 9 from 81s-333.
r=(9s)/(5)-(37)/(5)_(9(9s-37))/(5)+5s=103
Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of 5.
r=(9s)/(5)-(37)/(5)_(9(9s-37))/(5)+5s*(5)/(5)=103
Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 5.
r=(9s)/(5)-(37)/(5)_(9(9s-37))/(5)+(5s*5)/(5)=103
Multiply 5s by 5 to get 25s.
r=(9s)/(5)-(37)/(5)_(9(9s-37))/(5)+(25s)/(5)=103
The numerators of expressions that have equal denominators can be combined. In this case, (9(9s-37))/(5) and ((25s))/(5) have the same denominator of 5, so the numerators can be combined.
r=(9s)/(5)-(37)/(5)_(9(9s-37)+(25s))/(5)=103
Simplify the numerator of the expression.
r=(9s)/(5)-(37)/(5)_(81s-333+25s)/(5)=103
Since 81s and 25s are like terms, add 25s to 81s to get 106s.
r=(9s)/(5)-(37)/(5)_(106s-333)/(5)=103
Multiply each term in the equation by 5.
r=(9s)/(5)-(37)/(5)_(106s-333)/(5)*5=103*5
Simplify the left-hand side of the equation by canceling the common factors.
r=(9s)/(5)-(37)/(5)_106s-333=103*5
Multiply 103 by 5 to get 515.
r=(9s)/(5)-(37)/(5)_106s-333=515
Since -333 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 333 to both sides.
r=(9s)/(5)-(37)/(5)_106s=333+515
Add 515 to 333 to get 848.
r=(9s)/(5)-(37)/(5)_106s=848
Divide each term in the equation by 106.
r=(9s)/(5)-(37)/(5)_(106s)/(106)=(848)/(106)
Simplify the left-hand side of the equation by canceling the common factors.
r=(9s)/(5)-(37)/(5)_s=(848)/(106)
Simplify the right-hand side of the equation by simplifying each term.
r=(9s)/(5)-(37)/(5)_s=8
Replace all occurrences of s with the solution found by solving the last equation for s. In this case, the value substituted is 8.
r=(9(8))/(5)-(37)/(5)_s=8
Multiply 9 by 8 in the numerator.
r=(9*8)/(5)-(37)/(5)_s=8
Multiply 9 by 8 to get 72.
r=(72)/(5)-(37)/(5)_s=8
Complete the multiplication to produce a denominator of 5 in each expression.
r=-(37)/(5)+(72)/(5)_s=8
Combine the numerators of all fractions that have common denominators.
r=(-37+72)/(5)_s=8
Add 72 to -37 to get 35.
r=(35)/(5)_s=8
Reduce the expression (35)/(5) by removing a factor of 5 from the numerator and denominator.
r=7_s=8
This is the solution to the system of equations.
r=7_s=8
|
|
|
| |
