Solve by elimination method.
0.3x – 0.2y = 4
0.5x + 0.5y = 85/19
I believe you start by multiplying the 0.2 by 0.5 and the 0.5y by 0.2. That way you can eliminiate the y. Then you solve for x. from there, you can solve for your y value........
Hope that helps!
0.3x – 0.2y = 4
Multiply both sides by 10.
3x - 2y = 40
Add 2y to both sides and divide by 3.
x =(2y+40)/3
Substitute that value for x in the second equation and solve for y. Put the value for y in the above equation to solve for x. Check by putting both values in the second equation.
I hope this helps. Thanks for asking.
To solve the given system of equations using the elimination method, follow these steps:
Step 1: Multiply both sides of each equation by a coefficient such that the coefficients of one of the variables in both equations will be opposite in sign. In this case, we'll aim to eliminate either x or y by making the coefficients of one of the variables equal.
To eliminate the y-variable, we can multiply both sides of the first equation by 5 and the second equation by 2. This will result in the coefficients of y becoming opposite:
Equation 1: (5)(0.3x) - (5)(0.2y) = (5)(4)
1.5x - 1y = 20 (multiply each term by 5)
Equation 2: (2)(0.5x) + (2)(0.5y) = (2)(85/19)
x + y = 170/19 (multiply each term by 2)
Step 2: Now, we have two equations with opposite coefficients for the y-variable. Add the equations together to eliminate y.
1.5x - y = 20 (Equation 1)
x + y = 170/19 (Equation 2)
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2.5x = 380/19
Step 3: Simplify the resulting equation.
To eliminate the fraction, multiply both sides of the equation by the reciprocal of the fraction's denominator.
2.5x = 380/19
(19/380)(2.5x) = (19/380)(380/19)
x = 20
Step 4: Substitute the found value of x back into one of the original equations to solve for y.
Using Equation 2:
x + y = 170/19
20 + y = 170/19
To isolate y, subtract 20 from both sides:
y = 170/19 - 20
To simplify the right side, you can convert 20 to 380/19:
y = 170/19 - 380/19
Combine the fractions:
y = (170 - 380)/19
y = -210/19
So the solution to the system of equations is x = 20 and y = -210/19.