three times a first number decreased by a second number is 25. the first number increased by four times the second number is -22. find the numbers
3x-y=25
x+4y=-22
3x-y=25
-3x-12y=66
-13y=91
y=-7
x+4(-7)=-22
x=6
first number -- x
second number ---y
translation:
" three times a first number decreased by a second number is 25" ---> 3x - y = 25
" the first number increased by four times the second number is -22" ---> x + 4y = -22
form 2nd equation: x = -4y - 22
sub into 1st equation:
3(-4y-22) - y = 25
-12y - 66 - y = 25
-13y = 91
y = -7
then x = 28-22 = 6
First number is 6, then second is -7
check:
3(6) - (-7) = 25
6 + 4(-7) = -22 , looks good
Three times a number, decreased by 28.
the certain is decreased by 3
.what is the expression
To solve this problem, we'll set up a system of equations using the given information.
Let's assign variables to the two numbers:
Let the first number be represented by x.
Let the second number be represented by y.
Now, let's translate the given information into equations:
"Three times a first number decreased by a second number is 25":
3x - y = 25
"The first number increased by four times the second number is -22":
x + 4y = -22
We now have a system of equations:
1) 3x - y = 25
2) x + 4y = -22
To solve this system, we can use the method of substitution or elimination.
Using the method of substitution:
We solve one equation for one variable and substitute that expression into the other equation.
From equation 2, let's solve for x in terms of y:
x = -22 - 4y
Now let's substitute this expression for x in equation 1:
3(-22 - 4y) - y = 25
Simplify and solve for y:
-66 - 12y - y = 25
-13y - 66 = 25
-13y = 91
y = -7
Now, substitute the value of y into equation 2 to find the value of x:
x + 4(-7) = -22
x - 28 = -22
x = 6
Therefore, the first number (x) is 6, and the second number (y) is -7.