I need help to this mathe problems...
1.Elimination using Multiplication
x-5y=0
2x-3y=7
Find the value of x in one equation.
x = 5y
Then substitute that value for x in the second equation. Solve for y, then find the value of x. Insert both values into the equations to check your results.
I hope this helps. Thanks for asking.
To solve the system of equations using elimination by multiplication, follow these steps:
1. Multiply one or both equations by a suitable factor to make the coefficients of either x or y in both equations equal or opposite.
Let's multiply the first equation by 2, so the coefficients of x in both equations become 2.
2(x - 5y) = 0 becomes 2x - 10y = 0
2. Align the equations vertically and subtract one equation from the other to eliminate the variable.
(2x - 10y) - (2x - 3y) = 0 - 7
Simplifying the equation, we have:
-10y + 3y = -7
-7y = -7
3. Solve for y by dividing both sides of the equation by the coefficient of y (-7).
-7y / -7 = -7 / -7
y = 1
4. Substitute the value of y back into one of the original equations to solve for x.
Using the first equation:
x - 5(1) = 0
x - 5 = 0
x = 5
5. Check your answer by substituting the values of x and y into both original equations.
Checking the first equation:
5 - 5(1) = 0
5 - 5 = 0
0 = 0 (true)
Checking the second equation:
2(5) - 3(1) = 7
10 - 3 = 7
7 = 7 (true)
Therefore, the solution to the system of equations is x = 5 and y = 1.