solve the following simultaneous linear equation:
-5x+6y=44
9x+7y=-8
first one times 7
-35x + 42y = 308
second by 6
54x + 42y = - 48
subtract them ..
-89x = 356
x = -4
sub back in first
20 + 6y = 44
6y = 24
y = 4
so x= - 4 and y= 4
To solve the system of simultaneous linear equations:
-5x + 6y = 44 -- Equation 1
9x + 7y = -8 -- Equation 2
There are a few methods you can use, such as substitution, elimination, or matrix methods. Here, I'll explain how to solve this system using the method of substitution:
Step 1: Solve one of the equations for one variable.
Let's solve Equation 1 for x.
-5x + 6y = 44
We isolate x by adding 5x to both sides:
6y = 5x + 44
Divide both sides by 6:
y = (5x + 44) / 6
Step 2: Substitute the expression for y in terms of x into the other equation (Equation 2).
Replace y in Equation 2 with (5x + 44) / 6:
9x + 7((5x + 44) / 6) = -8
Step 3: Simplify and solve for x.
To eliminate the fraction, you can multiply all terms by 6:
6(9x) + 6(7((5x + 44) / 6)) = 6(-8)
54x + 7(5x + 44) = -48
Expand and simplify:
54x + 35x + 308 = -48
89x + 308 = -48
Subtract 308 from both sides:
89x = -356
Divide both sides by 89:
x = -356/89
x = -4
Step 4: Substitute the value of x back into one of the original equations (Equation 1) to find y.
-5x + 6y = 44
-5(-4) + 6y = 44
20 + 6y = 44
Subtract 20 from both sides:
6y = 24
y = 24/6
y = 4
Therefore, the solution to the simultaneous linear equations is x = -4 and y = 4.