The key insight here is that for the second equation, we can easily solve for a variable in term of the other variable.
Let's just add #y# to both sides to solve for #x# in terms of #y#. We get
#color(blue)(x=y+1)#
We can plug this value of #x# into the first equation in the system. We get
#3(y+1)+4y=10#
Distributing the #3# to both terms in the parenthesis, we get
#3y+3+4y=10#
Combining like terms, we now have
#7y+3=10#
Subtracting #3# from both sides, we get
#7y=7#
Dividing both sides by #7#, we find that
#color(red)(y=1)#
We can plug this value into the blue expression to get
#x=1+1#
#color(red)(=>x=2)#
Hope this helps!
A system of linear equations contains two or more equations e.g. y=0.5x+2 and y=x-2. The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.
Example
$$\left\{\begin{matrix} y=2x+2\\ y=x-1\: \: \: \end{matrix}\right.$$
Graph the equations in a coordinate plane
The two lines intersect in (-3, -4) which is the solution to this system of equations.
Video lesson
Find the solution of two equations by graphing
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- x+y+z=25,\:5x+3y+2z=0,\:y-z=6
- x+2y=2x-5,\:x-y=3
- 5x+3y=7,\:3x-5y=-23
- x^2+y=5,\:x^2+y^2=7
- xy+x-4y=11,\:xy-x-4y=4
- 3-x^2=y,\:x+1=y
- xy=10,\:2x+y=1
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