y =1/4x - 4 : y = -7/4x + 4
I need help with this one...has to be solved by elimination. Thanks
y = y
1 / 4 x - 4 = - 7 / 4 x + 4
Add 7 / 4 x to both sides
1 / 4 x - 4 + 7 / 4 x = - 7 / 4 x + 4 + 7 / 4 x
8 / 4 x - 4 = 4
2 x - 4 = 4
Add 4 to both sides
2 x - 4 + 4 = 4 + 4
2 x = 8
Divide both sides by 2
x = 8 / 2
x = 4
Replace this value in equation for y.
y = 1 / 4 x - 4 = x / 4 - 4 = 4 / 4 - 4 = 1 - 4 = - 3
OR
y = - 7 / 4 x + 4 = - 7 ∙ x / 4 + 4 = - 7 ∙ 4 / 4 + 4 = - 7 + 4 = - 3
Solution:
x = 4 , y = - 3
You can write this as:
( 4 , - 3 )
-x/4 + y = -4. Standard form.
Multiply both sides by 4:
Eq1: -x + 4y = -16.
7x/4 + y = 4.
Multiply both sides by 4:
Eq2: 7x + 4y = 16.
Multiply Eq1 by -1 and add Eq1 and Eq2:
x - 4y = 16
7x + 4y = 16
Sum: 8x = 32
X = 4.
In Eq1, replace X with 4 and solve for Y:
-4 + 4y = -16.
Y = -3.
To solve the system of equations using the elimination method, we need to eliminate one variable by adding or subtracting the two equations. In this case, we can eliminate the variable "y" by manipulating the second equation.
Given:
Equation 1: y = (1/4)x - 4
Equation 2: y = (-7/4)x + 4
Both equations are already in slope-intercept form (y = mx + b), with the constants (b values) being different. We can start by manipulating Equation 2 to make the coefficient of x the same as it is in Equation 1.
In Equation 2, since the coefficient of x is (-7/4), we can multiply the entire equation by 4 to eliminate the fraction:
4 * y = 4 * (-7/4)x + 4 * 4
4y = -7x + 16
Now we have the two equations:
Equation 1: y = (1/4)x - 4
Equation 2: 4y = -7x + 16
We can now set the two equations equal to each other:
(1/4)x - 4 = -7x + 16
Next, we can eliminate the fraction by multiplying through by the common denominator, which is 4:
4 * [(1/4)x - 4] = 4 * (-7x + 16)
x - 16 = -28x + 64
Now, move all the terms involving x to one side of the equation and the constants to the other side:
x + 28x = 64 + 16
29x = 80
Finally, solve for x by dividing both sides of the equation by 29:
x = 80/29
Now that we have the value of x, we can substitute it back into either of the original equations to solve for y. Let's substitute it into Equation 1:
y = (1/4)(80/29) - 4
Simplifying the equation:
y = 20/29 - 4
y = 20/29 - (4 * 29/29)
y = 20/29 - 116/29
y = -96/29
So the solution to the system of equations is x = 80/29 and y = -96/29.
multiply 1st eqn by 7
add to 2nd eqn to eliminate x
solve for y , then substitute back to find x