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Translate this word problem as a system of equations and then solve using substitution Find two numbers whose sum is 58 and whose difference is 16?
Suppose the two numbers are x and y.
Then x + y = 58 and x - y = 16
The second equation gives x = 16 + y
Substituting this value of x into the first equation gives
(16 + y) + y = 58
or 2y + 16 = 58 or 2y = 42 which gives y = 21.
Then x = 16 + y gives x = 16 + 21 = 37
So the soln is x = 37, y = 21
What else can I help you with?
What are two numbers that when multiplied are 180 and when added are 24?
204
What in the difference between a numerical and algebraic expression?
Numerical equations have only numbers and symbols, while algebraic equations have variables also.
The sum of two numbers is 92 their difference is 20 find the numbers?
Let the two numbers be m and n From the information given, we have two equation in two unknowns. We can solve this system using substitution. Here are the two equations. m+n=92 m-n=20 Now to use substitution, we must rewrite the second equation as m=n+20 and substitute it into the first n+n+20=92 or 2n=72 which tells us n=36 that means m=92-36 or 56. So the numbers are 36 and 56. Let's check 36+56=92 56-36=20
What two numbers add up to 34?
I think you have mistyped your question...
Find two numbers whose sum is 23 and whose difference is 7?
x + y = 23x - y = 7Add the equations:2x = 30x = 15Subtract the equations:2y = 16y = 8
What is the difference with equations with integers and equations with rational numbers?
It is a trivial difference. If you multiply every term in the equation with rational numbers by the common multiple of all the rational numbers then you will have an equation with integers.
What are two numbers that when multiplied are 180 and when added are 24?
204
What in the difference between a numerical and algebraic expression?
Numerical equations have only numbers and symbols, while algebraic equations have variables also.
When is the substitution method a better method than graphing for solving a system of linear equation?
The substitution method is often better than graphing for solving a system of linear equations when the equations are more complex or when the coefficients are not easily manageable for graphing. It is particularly advantageous when at least one equation can be easily solved for one variable, allowing for straightforward substitution. Additionally, substitution is more precise for finding exact solutions, especially when dealing with fractions or irrational numbers, where graphing may yield less accurate results. Finally, when the system has no clear intersection point or consists of more than two equations, substitution can simplify the process significantly.
If the sum of two numbers is 4 and their difference is -2 what are the numbers?
6
What The sum of 20 and their difference 4?
If the sum of two numbers is 20 and their difference is 4, you can set up the equations: ( x + y = 20 ) and ( x - y = 4 ). By solving these equations simultaneously, you find that ( x = 12 ) and ( y = 8 ). Thus, the two numbers are 12 and 8.
What is the difference between exponential functions and logarithmic functions?
Exponential and logarithmic functions are different in so far as each is interchangeable with the other depending on how the numbers in a problem are expressed. It is simple to translate exponential equations into logarithmic functions with the aid of certain principles.
What does it mean to solve a system of quadratic equations?
Solving a system of quadratic equations involves finding the values of the variables that satisfy all equations in the system simultaneously. This typically requires identifying the points of intersection between the curves represented by the quadratic equations on a graph. The solutions can be real or complex numbers and may include multiple pairs of values, depending on the nature of the equations. Techniques for solving these systems include substitution, elimination, or graphical methods.
What equals a sum of 7 and a difference of 1?
To find two numbers that equal a sum of 7 and a difference of 1, let’s denote the numbers as ( x ) and ( y ). From the information given, we can set up the equations: ( x + y = 7 ) and ( x - y = 1 ). Solving these equations, we find that ( x = 4 ) and ( y = 3 ). Thus, the two numbers are 4 and 3.
The sum of two numbers is 92 their difference is 20 find the numbers?
Let the two numbers be m and n From the information given, we have two equation in two unknowns. We can solve this system using substitution. Here are the two equations. m+n=92 m-n=20 Now to use substitution, we must rewrite the second equation as m=n+20 and substitute it into the first n+n+20=92 or 2n=72 which tells us n=36 that means m=92-36 or 56. So the numbers are 36 and 56. Let's check 36+56=92 56-36=20
What two numbers add up to 34?
I think you have mistyped your question...
Find two numbers whose sum is 23 and whose difference is 7?
x + y = 23x - y = 7Add the equations:2x = 30x = 15Subtract the equations:2y = 16y = 8
