Solve each system
x + 3y = 6
4x - 5y = 7
I need to know what x and y equal??
To solve the system of equations, we can use the method of elimination or substitution. Since the coefficient of x is 1 in the first equation, we will use the method of substitution.
Step 1: Solve one equation for one variable in terms of the other variable.
From the first equation, we can solve for x in terms of y:
x = 6 - 3y
Step 2: Substitute the expression of x in terms of y into the other equation.
Replace x in the second equation with (6 - 3y):
4(6 - 3y) - 5y = 7
Simplifying this equation gives:
24 - 12y - 5y = 7
24 - 17y = 7
Step 3: Solve the resulting equation for the remaining variable.
-17y = 7 - 24
-17y = -17
y = -17 / -17
y = 1
Step 4: Substitute the value of y into one of the original equations to solve for x.
Using the first equation: x + 3(1) = 6
x + 3 = 6
x = 6 - 3
x = 3
Therefore, the solution to the system of equations is x = 3 and y = 1.