solving using the solution method.
x+10y=41
x+9y=37
=
I assume you mean the substitution method:
Eq1: X + 10Y = 41.
Eq2: X + 9Y = 37.
Multiply both sides of Eq1 by -1 and
add the 2 Eqs:
-X - 10Y = -41.
X + 9Y = 37.
Sum: 0 - Y = -4,
Y = 4.
In Eq2, substitute 4 for Y:
X + 9*4 = 37,
X = 37 - 36 = 1.
Solution Set = (X,Y) = (1,4).
Substitution Method:
Eq1: X + 10Y = 41.
Eq2: X + 9Y = 37.
In Eq1, solve for X and get:
X = -10Y + 41,
In Eq2,substitute -10Y + 41 for X:
(-10Y+41) + 9Y = 37,
-Y = 37 - 41 = -4,
Y = 4.
In Eq1, substitute 4 for Y:
X + 9*4 = 37,
X = 37 - 36 = 1.
Solution Set = (X,Y) = (1,4).
To solve the system of equations using the solution method:
Step 1: Choose one of the equations and solve for one variable in terms of the other variable. Let's choose the second equation (x + 9y = 37). Solve for x:
x = 37 - 9y
Step 2: Substitute the expression for x obtained in Step 1 into the other equation. We will substitute x = 37 - 9y into the first equation (x + 10y = 41):
(37 - 9y) + 10y = 41
Step 3: Simplify the equation and solve for y:
37 - 9y + 10y = 41
37 + y = 41
y = 41 - 37
y = 4
Step 4: Substitute the value of y found in Step 3 back into one of the original equations to solve for x. Let's use the second equation (x + 9y = 37):
x + 9(4) = 37
x + 36 = 37
x = 37 - 36
x = 1
Step 5: Check the solution by substituting the values of x and y into the other equation:
1 + 10(4) = 41
1 + 40 = 41
41 = 41
Both sides of the equation are equal, so the solution (x, y) = (1, 4) satisfies both equations.