How can I do x+5y=10
-2x-6y=-8
Look for a term in either equation that has a coefficient of 1 in front of a variable, then solve for that variable.
e.g. in x + 5y = 10, x = 10-5y
now sub that into the other equation ....
-2(10-5y) - 6y = -8
-20 + 10y - 6y = -8
4y = 12
y = 3
back into x = 10-5y
x = 10 - 15 = -5
in this case, elimination would have worked just as simple
-2x - 6y = -8 ----> x + 3y = 4
subtract the first: x + 5y = 10
2y = 6, y = 3
in x+5y = 10
x + 15 = 10
x = -5
Eq1: x + 5y = 10
Eq2: -2x - 6y = -8
Multiply both sides ofEq1 by 2 and add the Eqs:
2x + 10y = 20
-2x - 6y = -8
Sum: 4y = 12,
Y = 3.
In Eq1, replace Y with 3 and solve for X:
x + 5*3 = 10,
X = -5.
To solve the system of equations x + 5y = 10 and -2x - 6y = -8, we can use the method of substitution or the method of elimination. Let's use the method of elimination:
Step 1: Multiply the first equation by 2.
2(x + 5y) = 2(10)
This simplifies to:
2x + 10y = 20
Step 2: Now, we need to add the two equations together to eliminate the variable x.
(2x + 10y) + (-2x - 6y) = 20 + (-8)
Simplifying:
2x - 2x + 10y - 6y = 12
4y = 12
Step 3: Divide both sides of the equation by 4 to solve for y.
4y/4 = 12/4
y = 3
Step 4: Substitute the value of y back into either of the original equations to solve for x. Let's use the first equation.
x + 5(3) = 10
x + 15 = 10
Subtract 15 from both sides:
x = 10 - 15
x = -5
So, the solution to the system of equations x + 5y = 10 and -2x - 6y = -8 is x = -5 and y = 3.