solve using the elimination method
x+7y=58
-x+4y=30
Add the two equations.
11y = 88
Solve for y. Insert value in one equation to find x. Check by inserting both values into other equation.
To solve the system of equations using the elimination method, follow these steps:
Step 1: Multiply one or both of the equations by a constant if necessary to make the coefficients of x or y in one equation equal to the coefficients in the other equation. Let's multiply the first equation by 1 to leave it unchanged.
Equation 1: x + 7y = 58
Equation 2: -x + 4y = 30
Step 2: Add the corresponding sides of the equations together to eliminate one variable. In this case, we'll add the left sides and the right sides separately.
Equation 1: (x + 7y) = 58
Equation 2: (-x + 4y) = 30
Adding these equations gives us:
(x + 7y) + (-x + 4y) = 58 + 30
Simplifying further:
x - x + 7y + 4y = 88
Simplifying again:
11y = 88
Step 3: Solve for the remaining variable. Divide both sides of the equation by 11 to isolate y:
11y / 11 = 88 / 11
y = 8
Step 4: Substitute the value of y into either of the original equations to solve for x. Let's choose the first equation:
x + 7y = 58
x + 7(8) = 58
x + 56 = 58
Step 5: Solve for x:
x + 56 - 56 = 58 - 56
x = 2
So, the solution to the system of equations is x = 2 and y = 8.