0.3x - 0.2y = 4
0.5x + 0.5y = 45/23 How to eliminate?
multiply the top equation by 5
multiply the bottom equation by 2
Then add the equations.
Multiply the first equatuon by 2.5. That will give you
0.75 x - 0.5 y = 10
Now add that to
0.5x + 0.5y = 45/23
Add the last two equations and you get
1.25 x = 11 22/23
Solve for x. Then use any previous equation to get y.
To eliminate either the x or the y terms in the system of equations, you can use the method of elimination. Here's how you can proceed:
Step 1: Multiply both sides of the first equation by 10 to make the coefficients of x and y whole numbers:
10 * (0.3x - 0.2y) = 10 * 4
3x - 2y = 40 (Equation 1)
Step 2: Multiply both sides of the second equation by 2 to make the coefficients of x and y whole numbers:
2 * (0.5x + 0.5y) = 2 * (45/23)
x + y = 90/23 (Equation 2)
Now the system of equations becomes:
3x - 2y = 40 (Equation 1)
x + y = 90/23 (Equation 2)
To eliminate one variable, you need to ensure that the coefficients of either x or y in both equations are the same. In this case, we'll focus on eliminating y.
Step 3: Multiply both sides of Equation 2 by 2 to make the coefficient of y the same as the coefficient of y in Equation 1:
2 * (x + y) = 2 * (90/23)
2x + 2y = 180/23
The system of equations now becomes:
3x - 2y = 40 (Equation 1)
2x + 2y = 180/23 (Equation 3)
Step 4: Add Equation 1 and Equation 3 together:
(3x - 2y) + (2x + 2y) = 40 + (180/23)
When you simplify the equation, the y terms will be eliminated:
3x + 2x - 2y + 2y = 40 + (180/23)
5x = 40 + (180/23)
To solve for x, combine the numbers on the right side of the equation:
5x = 920/23 + 180/23
5x = 1100/23
To isolate x, divide both sides of the equation by 5:
(5x)/5 = (1100/23)/5
x = (1100/23) * (1/5)
x = 220/23
Now that you have the value of x, you can substitute it back into one of the original equations to solve for y.
Let's use Equation 2:
x + y = 90/23
Substituting x = 220/23:
(220/23) + y = 90/23
To solve for y, solve the equation for y by isolating it:
y = 90/23 - 220/23
y = (90 - 220)/23
y = -130/23
So, the solution for the system of equations is:
x = 220/23
y = -130/23