i need to know how to solve certain problems like this
4x=2y-10
x+2y=5
i need examples of this and shown to me step by step
4x=2y-10
[step 1] -2y -2y
-2y+4x=-10
[step 2] -4x -4x
-2y=-4x-10
[step 3] divide both sides by -2
y=2x+5 «answer!!
With first equation get x alone on one side.
x = .5y - 2.5
Substitute that value for x in the second equation and solve for y. Put that y value into the first equation to find value of x. To check, put both values into the second equation.
I hope this helps a little more. Thanks for asking.
To solve this system of equations, you can use the method of elimination or substitution. I will explain both methods step by step using your example equations:
Method 1: Elimination
Step 1: Multiply one or both equations by suitable constants to make the coefficients of one of the variables or their negatives equal.
In this case, we can eliminate the y variable by multiplying the second equation by 2:
Original equations:
4x = 2y - 10
x + 2y = 5
Multiply the second equation by 2:
2(x + 2y) = 2(5)
2x + 4y = 10
Step 2: Add or subtract the modified equations to eliminate the common variable.
Subtract the modified equation from the first equation:
4x - 2x = (2y - 10) - (2x + 4y)
2x - 2x + 10y = -10
Simplify:
10y = -10
Step 3: Solve for the remaining variable.
Divide both sides of the equation by 10:
y = -1
Step 4: Substitute the value of y into one of the original equations to solve for the other variable.
Substitute y = -1 into the second original equation:
x + 2(-1) = 5
x - 2 = 5
x = 7
Solution: The solution to the system of equations is x = 7 and y = -1.
Method 2: Substitution
Step 1: Solve one equation for one variable in terms of the other variable.
In this case, solve the second equation for x:
x = 5 - 2y
Step 2: Substitute this expression for x into the other equation and solve for the remaining variable.
Substitute x = 5 - 2y into the first equation:
4(5 - 2y) = 2y - 10
Simplify:
20 - 8y = 2y - 10
Step 3: Solve for y.
Combine like terms:
-10y = -30
Divide both sides of the equation by -10:
y = 3
Step 4: Substitute the value of y back into one of the original equations to solve for the other variable.
Substitute y = 3 into the second original equation:
x + 2(3) = 5
x + 6 = 5
x = -1
Solution: The solution to the system of equations is x = -1 and y = 3.
Both methods lead to the same solution, showing the intersection point of the two lines on the coordinate plane where they coincide.