use substitution method to find x and y for 7x + 5y = -31 and -4x + y = 37
(1) 7x + 5y = -31
(2) -4x + y = 37
first we choose an equation (either of the two) and represent one of the variables in terms of the other,, in this case we choose (2), and represent y in terms of x:
-4x + y = 37
y = 37 + 4x
we then substitute this equation to (1):
7x + 5y = -31
7x + 5(37 + 4x) = -31
7x + 185 + 20x = -31
27x = -216
x = -8
substitute this value of x to either equation:
-4(-8) + y = 37
y = 5
so there,, :)
To solve the system of equations using the substitution method, we can solve one equation for one variable and substitute that expression into the other equation. Let's solve the second equation for y:
-4x + y = 37
Rearrange the equation to solve for y:
y = 4x + 37
Now we can substitute this expression for y into the first equation:
7x + 5(4x + 37) = -31
Simplify the equation:
7x + 20x + 185 = -31
Combine like terms:
27x + 185 = -31
Subtract 185 from both sides:
27x = -216
Divide both sides by 27:
x = -8
Now that we have the value of x, we can substitute it back into either equation to find the value of y. Let's substitute it into the second equation:
-4(-8) + y = 37
32 + y = 37
Subtract 32 from both sides:
y = 5
Therefore, the solution to the system of equations is x = -8 and y = 5.
To solve the system of equations using the substitution method, we'll solve one equation for one variable and substitute it into the other equation. Let's start by isolating y in the second equation (-4x + y = 37):
1. Solve for y:
y = 4x + 37
Now, substitute this expression for y in the first equation (7x + 5y = -31):
2. Substitute:
7x + 5(4x + 37) = -31
Distribute the 5:
7x + 20x + 185 = -31
Combine like terms:
27x + 185 = -31
To isolate x, we'll subtract 185 from both sides:
27x + 185 - 185 = -31 - 185
Simplify:
27x = -216
Next, divide both sides by 27 to solve for x:
27x/27 = -216/27
Simplify:
x = -8
Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the second equation (-4x + y = 37):
3. Substitute x = -8:
-4(-8) + y = 37
Simplify:
32 + y = 37
To isolate y, we'll subtract 32 from both sides:
32 + y - 32 = 37 - 32
Simplify:
y = 5
So, the solution to the system of equations is x = -8 and y = 5.