4x+y=42
6x-5y=50
Solve using the substitution method.
To solve the given system of equations using the substitution method, follow these steps:
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve the first equation, 4x + y = 42, for y:
y = 42 - 4x
Step 2: Substitute the expression for the variable obtained in step 1 into the other equation.
Substitute y = 42 - 4x into the second equation, 6x - 5y = 50:
6x - 5(42 - 4x) = 50
Step 3: Simplify and solve for x.
Distribute -5 to the terms inside the parentheses:
6x - 210 + 20x = 50
Combine like terms:
26x - 210 = 50
Add 210 to both sides:
26x = 260
Divide both sides by 26:
x = 10
Step 4: Substitute the value of x back into either of the original equations to solve for y.
We'll use the first equation, 4x + y = 42:
4(10) + y = 42
40 + y = 42
Subtract 40 from both sides:
y = 2
Therefore, the solution to the system of equations is x = 10 and y = 2.
y=42-4x
substitute that into the other equation
6x-5(42-4x) = 50
what do you get?