Find the solution to this system of equations

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

Our online expert tutors can answer this problem

Get step-by-step solutions from expert tutors as fast as 15-30 minutes. Your first 5 questions are on us!

Number Line

How do you find the solution to a system of equations?

What is the solution to the system of equations y 3x 2 5x 2y 15?

What are the 3 solutions to systems of equations?

How do I find the solution to a system of equations by substitution?