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Question 392551: Solve. Use two variables and two equations.
1.The sum of two numbers is 35. One number is 4 times the other. Find the numbers.
2.One number is 5 more than another number. The sum of the two numbers is 43. Find the numbers.
3.One number us 5 times another number. It is also 3 more than twice the other number. Find the numbers.
4.Ellen is 5 years older than Trudy. Their ages total 39. How old is each person?
5. In a game of bowling, Buds score was 12 more than Jans. Their combined score was 328. Find their scores.
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! x+y=35_x=4y
Since y does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting y from both sides.
x=-y+35_x=4y
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is -y+35.
x=-y+35_(-y+35)=4y
Remove the parentheses around the expression -y+35.
x=-y+35_-y+35=4y
Since 4y contains the variable to solve for, move it to the left-hand side of the equation by subtracting 4y from both sides.
x=-y+35_-y+35-4y=0
Since -y and -4y are like terms, subtract 4y from -y to get -5y.
x=-y+35_-5y+35=0
Since 35 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 35 from both sides.
x=-y+35_-5y=-35
Divide each term in the equation by -5.
x=-y+35_-(5y)/(-5)=-(35)/(-5)
Simplify the left-hand side of the equation by canceling the common factors.
x=-y+35_y=-(35)/(-5)
Simplify the right-hand side of the equation by simplifying each term.
x=-y+35_y=7
Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is 7.
x=-(7)+35_y=7
Multiply -1 by the 7 inside the parentheses.
x=-7+35_y=7
Add 35 to -7 to get 28.
x=28_y=7
This is the solution to the system of equations.
x=28_y=7
x+y=43_x=5+y
Since y does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting y from both sides.
x=-y+43_x=y+5
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is -y+43.
x=-y+43_(-y+43)=y+5
Remove the parentheses around the expression -y+43.
x=-y+43_-y+43=y+5
Since y contains the variable to solve for, move it to the left-hand side of the equation by subtracting y from both sides.
x=-y+43_-y+43-y=5
Since -y and -y are like terms, subtract y from -y to get -2y.
x=-y+43_-2y+43=5
Since 43 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 43 from both sides.
x=-y+43_-2y=-43+5
Add 5 to -43 to get -38.
x=-y+43_-2y=-38
Divide each term in the equation by -2.
x=-y+43_-(2y)/(-2)=-(38)/(-2)
Simplify the left-hand side of the equation by canceling the common factors.
x=-y+43_y=-(38)/(-2)
Simplify the right-hand side of the equation by simplifying each term.
x=-y+43_y=19
Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is 19.
x=-(19)+43_y=19
Multiply -1 by the 19 inside the parentheses.
x=-19+43_y=19
Add 43 to -19 to get 24.
x=24_y=19
This is the solution to the system of equations.
x=24_y=19
y=5x_y=2x+3
Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is 5x.
y=5x_(5x)=2x+3
Remove the parentheses around the expression 5x.
y=5x_5x=2x+3
Since 2x contains the variable to solve for, move it to the left-hand side of the equation by subtracting 2x from both sides.
y=5x_5x-2x=3
Since 5x and -2x are like terms, add -2x to 5x to get 3x.
y=5x_3x=3
Divide each term in the equation by 3.
y=5x_(3x)/(3)=(3)/(3)
Simplify the left-hand side of the equation by canceling the common factors.
y=5x_x=(3)/(3)
Simplify the right-hand side of the equation by simplifying each term.
y=5x_x=1
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is 1.
y=5(1)_x=1
Multiply 5 by each term inside the parentheses.
y=5_x=1
This is the solution to the system of equations.
y=5_x=1
x+y=39_x=y+5
Since y does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting y from both sides.
x=-y+39_x=y+5
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is -y+39.
x=-y+39_(-y+39)=y+5
Remove the parentheses around the expression -y+39.
x=-y+39_-y+39=y+5
Since y contains the variable to solve for, move it to the left-hand side of the equation by subtracting y from both sides.
x=-y+39_-y+39-y=5
Since -y and -y are like terms, subtract y from -y to get -2y.
x=-y+39_-2y+39=5
Since 39 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 39 from both sides.
x=-y+39_-2y=-39+5
Add 5 to -39 to get -34.
x=-y+39_-2y=-34
Divide each term in the equation by -2.
x=-y+39_-(2y)/(-2)=-(34)/(-2)
Simplify the left-hand side of the equation by canceling the common factors.
x=-y+39_y=-(34)/(-2)
Simplify the right-hand side of the equation by simplifying each term.
x=-y+39_y=17
Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is 17.
x=-(17)+39_y=17
Multiply -1 by the 17 inside the parentheses.
x=-17+39_y=17
Add 39 to -17 to get 22.
x=22_y=17
This is the solution to the system of equations.
x=22_y=17
x+y=328_x=y+12
Since y does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting y from both sides.
x=-y+328_x=y+12
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is -y+328.
x=-y+328_(-y+328)=y+12
Remove the parentheses around the expression -y+328.
x=-y+328_-y+328=y+12
Since y contains the variable to solve for, move it to the left-hand side of the equation by subtracting y from both sides.
x=-y+328_-y+328-y=12
Since -y and -y are like terms, subtract y from -y to get -2y.
x=-y+328_-2y+328=12
Since 328 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 328 from both sides.
x=-y+328_-2y=-328+12
Add 12 to -328 to get -316.
x=-y+328_-2y=-316
Divide each term in the equation by -2.
x=-y+328_-(2y)/(-2)=-(316)/(-2)
Simplify the left-hand side of the equation by canceling the common factors.
x=-y+328_y=-(316)/(-2)
Simplify the right-hand side of the equation by simplifying each term.
x=-y+328_y=158
Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is 158.
x=-(158)+328_y=158
Multiply -1 by the 158 inside the parentheses.
x=-158+328_y=158
Add 328 to -158 to get 170.
x=170_y=158
This is the solution to the system of equations.
x=170_y=158
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