0.3x-0.2y=4
0.5x+0.3y=-7/17
Can anyone Please help me solve using the elimination system..... Someone tried to explain it but I still do not get it at all
Of course! I can help you solve this system of equations using the elimination method. The goal of the elimination method is to eliminate one variable by adding or subtracting the equations. Here's how to do it step by step:
Step 1: Multiply both equations by appropriate numbers to make the coefficients of one variable (either x or y) in both equations the same in magnitude but opposite in sign.
Let's focus on eliminating the variable y. To make the coefficients of y the same in magnitude but opposite in sign, we need to multiply the first equation by 3 and the second equation by 2. This will give us:
Equation 1: 3(0.3x) - 3(0.2y) = 3(4) => 0.9x - 0.6y = 12
Equation 2: 2(0.5x) + 2(0.3y) = 2(-7/17) => 1x + 0.6y = -14/17
Step 2: Add or subtract the modified equations to eliminate the variable y.
To eliminate y, we can add the modified Equation 1 to the modified Equation 2:
0.9x - 0.6y + 1x + 0.6y = 12 - 14/17
Simplifying the equation, we have:
1.9x = 12 - 14/17
Step 3: Solve for x.
To solve for x, we need to simplify the equation and isolate x. Let's find a common denominator for 12 and 14/17, which is 17:
1.9x = (12 * 17) - 14
1.9x = 204 - 14
1.9x = 190
Dividing both sides of the equation by 1.9, we get:
x ≈ 190 / 1.9
x ≈ 100
Step 4: Substitute the value of x back into one of the original equations to solve for y.
Let's substitute x = 100 into the first equation:
0.3(100) - 0.2y = 4
30 - 0.2y = 4
Now, isolate y by subtracting 30 from both sides:
-0.2y = 4 - 30
-0.2y = -26
Divide both sides by -0.2:
y = -26 / -0.2
y = 130
So the solution to the system of equations is x = 100, y = 130.