solve the system equations
-x+6y=13
4x-10y=-10
To solve this system of equations, we can use the method of substitution.
Step 1: Solve one equation for one variable in terms of the other variable.
Rearranging the first equation, we have:
-x + 6y = 13
⇒ -x = 13 - 6y
⇒ x = -13 + 6y
Step 2: Substitute the expression found for x into the second equation.
Substituting x = -13 + 6y into the second equation, we have:
4(-13 + 6y) - 10y = -10
-52 + 24y - 10y = -10
14y = 42
y = 42/14
y = 3
Step 3: Substitute the value of y back into one of the original equations to find the value of x.
Using the first equation:
-x + 6(3) = 13
-x + 18 = 13
-x = 13 - 18
-x = -5
x = 5
Therefore, the solution to the system of equations is x = 5 and y = 3.
To solve the system of equations:
1. Multiply the first equation by 4 and the second equation by -1 to make the coefficients of x equal.
-4x + 24y = 52
-4x + 10y = 10
2. Subtract the second equation from the first equation to eliminate x.
(-4x + 24y) - (-4x + 10y) = 52 - 10
-4x + 24y + 4x - 10y = 42y = 42
Simplify: 14y = 42
3. Divide both sides of the equation by 14 to solve for y.
14y / 14 = 42 / 14
y = 3
4. Substitute the value of y into one of the original equations (let's use the first equation) to solve for x.
-x + 6(3) = 13
-x + 18 = 13
-x = 13 - 18
-x = -5
5. Multiply both sides of the equation by -1 to solve for x.
-1(-x) = -1(-5)
x = 5
Therefore, the solution to the system of equations is x = 5 and y = 3.
To solve the system of equations:
Step 1: We will use the method of elimination to eliminate one variable.
Multiply the first equation by 4 and the second equation by -1 to eliminate the x term:
-4x + 24y = 52
-4x + 10y = 10
Step 2: Subtract the second equation from the first equation to eliminate the x term:
(-4x + 24y) - (-4x + 10y) = 52 - 10
-4x + 24y + 4x - 10y = 42
14y = 42
Step 3: Divide both sides of the equation by 14 to solve for y:
14y/14 = 42/14
y = 3
Step 4: Substitute the value of y back into either of the original equations and solve for x:
-x + 6(3) = 13
-x + 18 = 13
-x = 13 - 18
-x = -5
x = 5
Step 5: The solution to the system of equations is x = 5 and y = 3.