Solve the system of equations. 3x+6y=21 –5x+2y=13 (1 point)
To solve the system of equations, we can use the method of substitution.
First, let's solve the first equation for x:
3x + 6y = 21
3x = 21 - 6y
x = (21 - 6y)/3
x = 7 - 2y
Now, we can substitute this expression for x into the second equation:
-5(7 - 2y) + 2y = 13
-35 + 10y + 2y = 13
12y = 48
y = 4
Now that we have the value of y, we can substitute it back into the expression for x:
x = 7 - 2(4)
x = 7 - 8
x = -1
Therefore, the solution to the system of equations is x = -1 and y = 4.
To solve the system of equations:
Step 1: Multiply the second equation by 3 to make the coefficients of x in both equations the same:
3*(-5x+2y) = 3*13
-15x + 6y = 39
Step 2: Now, you have two equations with the same coefficient for x, so add the two equations together:
(3x + 6y) + (-15x + 6y) = 21 + 39
-12x + 12y = 60
Step 3: Divide both sides of the equation by 12 to solve for y:
(-12x + 12y)/12 = 60/12
-x + y = 5
Step 4: Now, solve for x by substituting the value of y from Step 3 into either of the original equations. Let's use the first equation:
3x + 6(5) = 21
3x + 30 = 21
3x = 21 - 30
3x = -9
x = -9/3
x = -3
Step 5: Therefore, the solution to the system of equations is x = -3 and y = 5.
To solve the system of equations:
3x + 6y = 21 ...(Equation 1)
-5x + 2y = 13 ...(Equation 2)
We can solve the system of equations using the method of substitution or elimination. Let's solve it using the method of substitution here:
Step 1: Solve one equation for one variable. Let's solve Equation 1 for x:
3x = 21 - 6y
x = (21 - 6y) / 3
x = 7 - 2y ...(Equation 3)
Step 2: Substitute x from Equation 3 into Equation 2:
-5(7 - 2y) + 2y = 13
-35 + 10y + 2y = 13
12y = 48
y = 4
Step 3: Substitute y = 4 into Equation 3 to find x:
x = 7 - 2(4)
x = 7 - 8
x = -1
Therefore, the solution to the system of equations is x = -1 and y = 4.