4x+y=2
-2x-3y=1
system of linear equations by substitution.
x=5
y=2
nope, putting in 5,2 in to the first equation is not - 2
Substitution
first equation: y=2-4x
into second:
-2x-3(2-4x)=1
-2x+12x-6=1
10x=7
x= 7/10
then y=2-4*7/10=2-2.8= -0.8
check that.
To solve this system of equations, we can use a method called elimination or substitution. Let's use the elimination method.
First, let's multiply the first equation by -2 to make the coefficient of x in both equations opposite.
-2(4x + y) = -2(2)
-8x - 2y = -4
Now, we can add the two equations together to eliminate the x variable.
(-8x - 2y) + (-2x - 3y) = -4 + 1
-10x - 5y = -3
Simplifying the equation further, we get:
-10x - 5y = -3
Now, we can solve this equation for either variable. Let's solve it for y.
-5y = -3 + 10x
-5y = 10x - 3
Divide both sides of the equation by -5.
y = (10x - 3)/-5
y = -2x + 3/5
Now that we have the equation for y in terms of x, we can substitute this value back into one of the original equations to solve for x.
Let's substitute y = -2x + 3/5 into the first equation:
4x + (-2x + 3/5) = 2
Combine like terms:
2x + 3/5 = 2
Subtract 3/5 from both sides:
2x = 2 - 3/5
2x = 10/5 - 3/5
2x = 7/5
Divide both sides by 2:
x = (7/5)/2
x = 7/10
So the solution of the system of equations is x = 7/10.
To find y, substitute this value of x back into one of the original equations:
4(7/10) + y = 2
28/10 + y = 2
y = 2 - 28/10
y = 20/10 - 28/10
y = -8/10
y = -4/5
Thus, the solution to the system of equations is x = 7/10 and y = -4/5.