So im struggling in math right now and i need help to do this can anyone please explain step by step on how to do this its solving systems of equations by substitution
5x-4y=-23
y=1/3x-5
This is a complicated one for sure.
Let's get rid of the fraction in the second problem by multiplying by 3
3y =x - 15 next solve for 3y + 15 = x. I did this step so that I could use substitution to solve.
Back to the first equation: 5( x ) -4y = -23
I substitute here 5( 3y + 15) -4y = -23 use the distributive law to get
15y + 75 -4y = -23
11y + 75 = -23
11y = -98 Solve for y and then substitute back into one of the original equations to find x. Finally, check your answers for x and y in both equations.
thank you this helped!
5x-4y=-23
y=1/3x-5 ---> 3y = x - 15 or x = 3y+15
sub into the first
5(3y+15) - 4y = -23
15y + 75 - 4y = -23
11y = -98
y = -98/11
then x = 3(-98/11) + 15 = -129/11
John is right as well
Sure! I'd be happy to walk you through the steps of solving a system of equations by substitution. Let's start by solving the given system of equations:
1) 5x - 4y = -23
2) y = (1/3)x - 5
The goal is to find the values of x and y that satisfy both equations.
Step 1: Solve one of the equations for one variable (preferably the one that is already isolated).
In this case, equation 2 is already solved for y: y = (1/3)x - 5. So, we can proceed to step 2.
Step 2: Substitute the expression found in Step 1 (y) into the other equation.
Replace y in equation 1 with (1/3)x - 5. The new equation will only have x as a variable.
5x - 4((1/3)x - 5) = -23
Step 3: Simplify and solve for x.
Distribute the -4 to both terms inside the parentheses:
5x - (4/3)x + 20 = -23
Combine like terms:
(15x - 4x)/3 + 20 = -23
(11x)/3 = -23 - 20
(11x)/3 = -43
Multiply both sides by 3 to eliminate the fraction:
11x = -129
Divide both sides by 11 to solve for x:
x = -129/11
Step 4: Substitute the found value of x back into one of the original equations to solve for y.
Let's use equation 2, y = (1/3)x - 5:
y = (1/3)(-129/11) - 5
Simplify:
y = -43/11 - 5
y = -43/11 - 55/11
y = -98/11
So, the solution to the system of equations is x = -129/11 and y = -98/11.
That's it! You have solved the system of equations using the substitution method.