Use the elimination method to solve these pairs of simultaneous equation
6x - 5y = -7
3x + 4y= 16
well, there are lots of choices but let's multiply the second one by 2 to get 6 x in each
6x - 5y = -7
6x + 8y= 32
---------------------- now subtract
0 - 13 y = -39
y = 39/13 = 3
now go back and use either for x
3x + 4y= 16
3 x + 4(3) = 16
3 x = 4
x = 4/3
==========================
now check by using in first one
6x - 5y = -7
6 (4/3) -5 (3) = -7????
8 -15 = - 7 ????
Yes, we won !!!
Explains clearer please
To solve these simultaneous equations using the elimination method, we need to eliminate one variable by multiplying one or both of the equations by suitable numbers so that the coefficients of either x or y will become the same or additive inverses.
Let's start by multiplying the second equation by 2 to make the coefficients of x opposite:
2 * (3x + 4y) = 2 * 16
6x + 8y = 32
Now we have:
6x - 5y = -7
6x + 8y = 32
Next, we need to eliminate the x variable. Subtract the first equation from the second equation:
(6x + 8y) - (6x - 5y) = 32 - (-7)
6x + 8y - 6x + 5y = 32 + 7
13y = 39
Dividing both sides of the equation by 13:
13y/13 = 39/13
y = 3
Now substitute the value of y into one of the original equations, let's use the first one:
6x - 5(3) = -7
6x - 15 = -7
6x = -7 + 15
6x = 8
Dividing both sides by 6:
6x/6 = 8/6
x = 4/3
So, the solution to the simultaneous equations is:
x = 4/3
y = 3
To solve the given system of equations using the elimination method, follow these steps:
Step 1: Choose a common coefficient for either x or y to eliminate when the equations are added or subtracted together.
Step 2: Multiply the equations by appropriate constants to make the coefficients of the same variable opposites.
Step 3: Add or subtract the equations to eliminate one of the variables.
Step 4: Solve the resulting equation for the remaining variable.
Step 5: Substitute the value of the solved variable back into one of the original equations and solve for the other variable.
Now let's apply these steps to the given system of equations.
Equation 1: 6x - 5y = -7
Equation 2: 3x + 4y = 16
Step 1: Choose a common coefficient to eliminate either x or y. In this case, let's eliminate y.
Step 2: Multiply the first equation by 4 and the second equation by 5 to make the coefficients of y opposite:
4 * (6x - 5y) = 4 * (-7) ---> 24x - 20y = -28
5 * (3x + 4y) = 5 * 16 ---> 15x + 20y = 80
Step 3: Add the equations to eliminate y:
(24x - 20y) + (15x + 20y) = -28 + 80
24x + 15x - 20y + 20y = 52
39x = 52
Step 4: Solve for x:
Divide both sides of the equation by 39:
39x / 39 = 52 / 39
x = 52 / 39
x = 4/3
Step 5: Substitute the value of x = 4/3 into one of the original equations, let's use Equation 1:
6x - 5y = -7
6(4/3) - 5y = -7
8 - 5y = -7
-5y = -7 - 8
-5y = -15
y = -15 / -5
y = 3
Therefore, the solution to the system of equations is x = 4/3 and y = 3.