Solve each system
x + 3y = 6
4x - 5y = 7
I need to know what x and y equal??
in this case I would use "substitution".
from the 1st: ----> x = 6-3y
sub that into the 2nd
4x - 5y = 7
4(6-3y) - 5y = 7
24 - 12y - 5y = 7
-17y = -17
y = 1
put that back into x = 6-3y
x = 6 -3(1) = 3
Good
To solve the system of equations:
Step 1: We will use the method of elimination. Multiply the first equation by 4 and the second equation by 1:
4(x + 3y) = 4(6)
1(4x - 5y) = 1(7)
Simplifying the equations:
4x + 12y = 24
4x - 5y = 7
Step 2: Subtract the second equation from the first equation to eliminate the x term:
(4x + 12y) - (4x - 5y) = 24 - 7
Simplifying the equation:
17y = 17
Step 3: Solve for y by dividing both sides by 17:
y = 1
Step 4: Substitute the value of y back into one of the original equations, let's use the first equation:
x + 3(1) = 6
Simplifying the equation:
x + 3 = 6
x = 6 - 3
x = 3
Therefore, the solution to the system of equations is x = 3 and y = 1.
To solve the system of equations, you can use the method of substitution or the method of elimination. Let's use the method of substitution.
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve the first equation, x + 3y = 6, for x:
x = 6 - 3y
Step 2: Substitute the expression for x into the second equation.
Replace x in the second equation, 4x - 5y = 7, with 6 - 3y:
4(6 - 3y) - 5y = 7
Step 3: Simplify and solve for y.
Distribute 4 to both terms inside the parentheses:
24 - 12y - 5y = 7
Combine like terms:
-17y + 24 = 7
Subtract 24 from both sides:
-17y = 7 - 24
-17y = -17
Divide both sides by -17:
y = 1
Step 4: Substitute the value of y back into one of the original equations to solve for x.
Let's use x + 3y = 6:
x + 3(1) = 6
x + 3 = 6
Subtract 3 from both sides to solve for x:
x = 6 - 3
x = 3
So the solution to the system of equations is x = 3 and y = 1.