Solve for x and
x+2y=10
3x-y=9
multiplly the first equation by .5
.5x+y=5
3x-y=9
add the equations
3.5x=14
x=4
now in the first equation use that x and solve for y.
To solve the system of equations, we can use one of several methods, such as substitution or elimination.
Let's solve it using the method of substitution:
Step 1: Solve one equation for one variable.
Let's solve the first equation, x + 2y = 10, for x:
x = 10 - 2y
Step 2: Substitute the expression for x in the second equation.
Replace x in the second equation, 3x - y = 9, with the expression we found for x in step 1:
3(10 - 2y) - y = 9
Step 3: Simplify and solve the resulting equation.
Distribute 3 into the parentheses:
30 - 6y - y = 9
Combine like terms:
-7y + 30 = 9
Step 4: Isolate the variable.
Subtract 30 from both sides of the equation:
-7y = 9 - 30
-7y = -21
Divide both sides by -7:
y = -21 / -7
y = 3
Step 5: Substitute the value of y back into one of the original equations to find x.
Let's substitute y = 3 into the first equation:
x + 2(3) = 10
x + 6 = 10
Subtract 6 from both sides:
x = 10 - 6
x = 4
Therefore, the solution to the system of equations is x = 4 and y = 3.