Note: Determine whether the solution to the new equation is a solution to the old system of equations by graphing. Use Desmos!
The solution to the original system of equations (is also or is not) a solution to the new equation.
Solve the system of equations by SUBSTITUTION.
6y + 5x = 8
x + 3y = -7
To solve the system of equations by substitution, we can start by solving one of the equations for one variable and then substituting it into the other equation.
Let's solve the second equation for x:
x = -7 - 3y
Now we can substitute this value of x into the first equation:
6y + 5(-7 - 3y) = 8
Simplifying the equation:
6y - 35 - 15y = 8
Combining like terms:
-9y - 35 = 8
Adding 35 to both sides:
-9y = 43
Dividing by -9:
y = -4.78 (rounded to two decimal places)
Now, substitute this value of y into the second equation to find x:
x + 3(-4.78) = -7
Simplifying the equation:
x - 14.34 = -7
Adding 14.34 to both sides:
x = 7.34 (rounded to two decimal places)
So the solution to the system of equations is x = 7.34 and y = -4.78.
Now, let's graph the original system of equations and the new equation in Desmos to check if the solution to the new equation is a solution to the old system of equations.