hi every one pls i dont know how to solve this question nor have the idea the quetion goes does: 4x+6y=21 7x-3y=3
7x-3y=3
14x-6y = 6
so, 6y = 14x-6
Now use that in the other equation and you have
4x+14x-6 = 21
18x = 27
x = 3/2
now use that to get y.
Divide Eq2 by 2 and you will get 7x - 3y = 3.
So the Eqs are identical. Therefore, we have an infinite number of solutions.
Eq1: 4x + 6y = 21.
Eq2: 7x - 3y = 3.
Multiply both sides of Eq2 by 2 and add the Eqs:
4x + 6y = 21
14x - 6y = 6
Sum: 18x = 27.
X = 1 1/2 = 3/2.
In Eq1, replace x with 3/2 and solve for y.
Please disregard my first response; I misunderstood the problem.
Hello! I can help you solve these two equations. This is called a system of equations. To solve it, we can use a method called elimination or substitution. Let's start with elimination.
The goal of the elimination method is to eliminate one variable by adding or subtracting the equations. Let's look at the given equations:
Equation 1: 4x + 6y = 21
Equation 2: 7x - 3y = 3
To eliminate one variable, we need to make the coefficients of either x or y the same in both equations. In this case, it would be easiest to eliminate y by making the coefficients the same.
Multiply Equation 1 by 3 and Equation 2 by 2 to make the coefficients of y the same:
Equation 1 (multiplied by 3): 12x + 18y = 63
Equation 2 (multiplied by 2): 14x - 6y = 6
Now, we can add the modified equations together to eliminate y:
(12x + 18y) + (14x - 6y) = 63 + 6
Combine like terms:
26x + 12y = 69
Now we have one equation with only x and y. To isolate one variable, we can solve this equation for either x or y.
Let's solve this equation for x:
26x + 12y = 69
26x = 69 - 12y
x = (69 - 12y)/26
Now we can substitute this expression for x into one of the original equations to find the value of y.
Let's use Equation 1:
4x + 6y = 21
4((69 - 12y)/26) + 6y = 21
Now we can simplify this equation and solve for y:
multiply both sides by 26 to eliminate denominators:
4(69 - 12y) + 156y = 546
Distribute:
276 - 48y + 156y = 546
Combine like terms:
108y = 270
Divide both sides by 108:
y = 270/108
Simplify:
y = 5/2 or y = 2.5
Now that we have the value of y, we can substitute it back into one of the original equations to find the value of x.
Let's substitute y = 2.5 into Equation 1:
4x + 6(2.5) = 21
4x + 15 = 21
Subtract 15 from both sides:
4x = 6
Divide both sides by 4:
x = 6/4
Simplify:
x = 3/2 or x = 1.5
So the solution to this system of equations is x = 1.5 and y = 2.5.
I hope this explanation helps!