Solve by using elimination:
7x - 2y =3
2x +y = 4
?????????????????
(1) 7x - 2y =3
(2) 2x + y = 4
look to see which variable is easier to get rid of. since the first equation has -2y, multiple the 2nd equation by 2, so that you get 2y. -2y + 2y = 0, so you will have eliminated the y variable
Multiple (2) by 2
2 (2x + y = 4) = 4x + 2y = 8
Add the two equations together
7x - 2y = 3
4x + 2y = 8
11x + 0 = 11
11x = 11
x = 1
Substitute x = 1 in either equation (1) or (2) to find y.
7x - 2y = 3
7(1) - 2y = 3
7 - 2y = 3
2y = 4
y = 2
To check
substitute x = 1, y = 2
in the other equation (1)
2x + y = 4
2(1) + 2 = 4
2 + 2 = 4
4 = 4
so it's correct
Thanks a lot:D
you're welcome
To solve this system of equations using the elimination method, we want to eliminate one variable by adding or subtracting the equations.
In this case, let's eliminate the y variable.
We can accomplish this by multiplying the second equation by 2, so the coefficients of the y terms will cancel each other out when added to the first equation.
The original equations are:
1) 7x - 2y = 3
2) 2x + y = 4
Let's multiply equation 2 by 2:
2 * (2x + y) = 2 * 4
4x + 2y = 8
Now we have:
3) 7x - 2y = 3
4) 4x + 2y = 8
Add equations 3 and 4 together:
(7x - 2y) + (4x + 2y) = 3 + 8
7x - 2y + 4x + 2y = 11
11x = 11
Divide both sides of the equation by 11 to solve for x:
11x/11 = 11/11
x = 1
Now substitute the value of x back into either of the original equations. Let's use equation 2 since it has the simplest coefficients:
2(1) + y = 4
2 + y = 4
Subtract 2 from both sides to solve for y:
y = 4 - 2
y = 2
Therefore, the solution to the system of equations is x = 1 and y = 2.