Solve:
3x + 7y + 5= 0
4x - 3y - 8 = 0
Find p; if:
px + y - 1= 0
I.
3x + 7y + 5 = 0
4x - 3y - 8 = 0
To solve, we can either use substitution or elimination method. For substitution, we choose one equation and represent one variable in terms of the other. Let's choose the first equation, and represent x in terms of y:
3x + 7y + 5 = 0
3x = -7y - 5
x = (-7/3)y - 5/3
then we substitute this to the 2nd equation:
4x - 3y - 8 = 0
4[(-7/3)y - 5/3] - 3y - 8 = 0
(-28/3 y - 20/3 - 3y - 8 = 0)*3
-28y - 20 - 9y - 24 = 0
-37y = 44
y = -44/37
substituting this back to either equations and solving for x,
x = 41/37
II.
px + y - 1= 0
px = 1 - y
p = (1-y)/x
hope this helps~ :)
To solve the system of equations:
3x + 7y + 5 = 0 ...(Equation 1)
4x - 3y - 8 = 0 ...(Equation 2)
We can use the method of substitution to find the values of x and y.
Step 1: Solve Equation 1 for x.
Rearrange Equation 1 to isolate x:
3x = -7y - 5
Step 2: Substitute the value of x from Step 1 into Equation 2.
Substitute -7y - 5 for x in Equation 2:
4(-7y - 5) - 3y - 8 = 0
Step 3: Simplify and solve for y.
Using the distributive property:
-28y - 20 - 3y - 8 = 0
-31y - 28 = 0
Simplifying further, we get:
-31y = 28
y = -28 / -31
y ≈ 0.9032 (rounded to four decimal places)
Step 4: Substitute the value of y into Equation 1 to solve for x.
Substitute 0.9032 for y in Equation 1:
3x + 7(0.9032) + 5 = 0
Multiply:
3x + 6.3224 + 5 = 0
3x + 11.3224 = 0
Rearrange the equation:
3x = -11.3224
x = -11.3224 / 3
x ≈ -3.7741 (rounded to four decimal places)
So, the values of x and y are approximately x ≈ -3.7741 and y ≈ 0.9032.
To find the value of p that satisfies the equation px + y - 1 = 0, we can substitute the values of x and y that we just found:
Substitute -3.7741 for x and 0.9032 for y:
p(-3.7741) + 0.9032 - 1 = 0
Simplifying further, we get:
-3.7741p + 0.9032 - 1 = 0
-3.7741p - 0.0968 = 0
Add 0.0968 to both sides:
-3.7741p = 0.0968
Divide both sides by -3.7741 to isolate p:
p = 0.0968 / -3.7741
So, p ≈ -0.0257 (rounded to four decimal places).
Therefore, p is approximately -0.0257 that satisfies the equation px + y - 1 = 0.