1.5x+4y=8
x+y=7
Please help me solve this system of equation and show your work.
I would multiply the 2nd equation by 4, then subtract ...
5x+4y=8
4x+4y=28
x = -20
sub into 2nd
-20 + y = 7
y = 27
x = -20 , y = 27
5x + 4y = 8
x + y = 7
Find x :
x = 7 - y
5(7 - y) + 4y = 8
35 - 5y + 4y = 8
-y = 8 - 35
y = 27
x = 7 + 27
x = 34
y = 27
x = 34
To solve the system of equations:
1.5x + 4y = 8 ---(1)
x + y = 7 ---(2)
We can use either the substitution method or the elimination method. Let's solve it using the elimination method.
First, let's multiply the second equation by 1.5 to make the coefficients of x in both equations the same. This will allow us to eliminate x when we subtract the two equations.
Multiply Equation (2) by 1.5:
1.5 * (x + y) = 1.5 * 7
1.5x + 1.5y = 10.5 ---(3)
Now, we have the following system of equations:
1.5x + 4y = 8 ---(1)
1.5x + 1.5y = 10.5 ---(3)
Next, subtract Equation (3) from Equation (1) to eliminate the x variable:
(1.5x + 4y) - (1.5x + 1.5y) = 8 - 10.5
1.5x - 1.5x + 4y - 1.5y = -2.5
Simplifying this equation gives us:
2.5y = -2.5
Now, divide both sides of the equation by 2.5 to solve for y:
y = -2.5 / 2.5
y = -1
Now substitute the value of y = -1 back into Equation (2) to solve for x:
x + (-1) = 7
x - 1 = 7
x = 7 + 1
x = 8
So, the solution to the system of equations is x = 8, y = -1.