5x-3y=3
2x-4y=-10
3x+y=(?)
a. -30
b. -13
c. -7
d. 7
e. 13
please answer and explain
since the solution to the first two equations is
x=3
y=4
you should have no trouble evaluating 3x+y
3(3)+4
9+4
13
answer e
thank you, Steve
but could you tell me how to solution the first two equation
substitution or elimination will work fine. Time to review your tools for solving systems of equations.
To find the value of 3x+y, you need to solve the given system of equations:
Equation 1: 5x - 3y = 3
Equation 2: 2x - 4y = -10
There are multiple methods to solve a system of equations, but here we will use the method of elimination:
Step 1: Multiply Equation 1 by 4 and Equation 2 by 3 to eliminate the x term.
Equation 1: 20x - 12y = 12
Equation 2: 6x - 12y = -30
Step 2: Subtract Equation 2 from Equation 1 to eliminate the y term.
(20x - 12y) - (6x - 12y) = 12 - (-30)
20x - 12y - 6x + 12y = 12 + 30
14x = 42
Step 3: Divide both sides of the equation by 14 to find the value of x.
14x / 14 = 42 / 14
x = 3
Step 4: Substitute the value of x = 3 into Equation 1 or Equation 2 to find the value of y.
Using Equation 1:
5x - 3y = 3
5(3) - 3y = 3
15 - 3y = 3
-3y = 3 - 15
-3y = -12
y = -12 / -3
y = 4
So, the value of x = 3 and y = 4.
Finally, we can substitute these values into the equation 3x + y to find the answer:
3x + y = 3(3) + 4 = 9 + 4 = 13
Therefore, the answer is e. 13.