How do I solve this using substitution method?
7x+9y=-38
-6x+y=50
solve either equation for x or y and substitute it into the other equation:
-6x+y = 50
y = 6x+50
so,
7x+9(6x+50) = -38
7x + 54x + 450 = -38
61x = -488
x = -8
now, use that value in either equation to get y:
y = 6(-8) + 50 = 2
To solve this system of equations using the substitution method, follow these steps:
Step 1: Solve one of the equations for one variable in terms of the other variable.
Let's solve the second equation for y:
-6x + y = 50
y = 6x + 50
Step 2: Substitute the expression for the variable found in step 1 into the other equation.
Replace y in the first equation with 6x + 50:
7x + 9(6x + 50) = -38
Step 3: Simplify and solve for x.
Distribute the 9 to each term in the parentheses:
7x + 54x + 450 = -38
Combine like terms on the left side:
61x + 450 = -38
Move the constant term to the right side:
61x = -38 - 450
61x = -488
Divide by 61 to isolate x:
x = -488/61
Simplify if necessary:
x = -8
Step 4: Substitute the value of x back into one of the original equations to solve for y.
Using the second equation:
-6(-8) + y = 50
48 + y = 50
Subtract 48 from both sides:
y = 50 - 48
y = 2
Step 5: Check your solution by substituting the values of x and y into the other equation.
Using the first equation:
7(-8) + 9(2) = -38
-56 + 18 = -38
-38 = -38
Therefore, the solution to the system of equations is x = -8 and y = 2.