I've been stuck on a problem with my homework for a couple of minutes now. We are doing Systems of Two Equations, using the substitution method. The problem is:
4y-6x+20=0
3=(18/5)x+(21/10)y
well, from the first equation,
y = (6x-20)/4
Substitute that into the second and you have
3 = (18/5)x + (21/10)(6x-20)/4
x = 2
So, y = -2
To solve this system of equations using the substitution method, you need to isolate one of the variables in one of the equations and substitute it into the other equation. Here's how you can go about it:
Equation 1: 4y-6x+20=0
Equation 2: 3=(18/5)x+(21/10)y
Step 1: Choose one of the equations to isolate a variable. Let's solve Equation 1 for y.
4y - 6x + 20 = 0
4y = 6x - 20
y = (6/4)x - 5
y = (3/2)x - 5
Step 2: Substitute the expression for y (from Step 1) into the other equation. Let's substitute (3/2)x - 5 for y in Equation 2.
3 = (18/5)x + (21/10)y
3 = (18/5)x + (21/10)((3/2)x - 5)
Step 3: Simplify the equation by distributing the fractions.
3 = (18/5)x + (21/10)(3/2)x - (21/10)(5)
Step 4: Continue simplifying the equation by multiplying and combining like terms.
3 = (18/5)x + (63/20)x - 21/2
Step 5: To get rid of the fractions, multiply the entire equation by the least common denominator (LCD), which is 20 in this case.
3(20) = (18/5)x(20) + (63/20)x(20) - (21/2)(20)
60 = 72x + 63x - 210
Step 6: Combine like terms again.
60 = 135x - 210
Step 7: Isolate the variable x by adding 210 to both sides of the equation.
60 + 210 = 135x
Step 8: Simplify.
270 = 135x
Step 9: Divide both sides of the equation by 135 to solve for x.
270/135 = x
2 = x
Step 10: Substitute the value of x back into the expression for y from Step 1 to solve for y.
y = (3/2)x - 5
y = (3/2)(2) - 5
y = 3 - 5
y = -2
Therefore, the solution to the system of equations is x = 2, y = -2.