Question

How many solutions are there to the following system of equations?

Answer 1

5x+3y=7
2x-y=2
Since 2x does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 2x from both sides.5x+3y=7
-y=-2x+2
Multiply each term in the equation by -1.5x+3y=7_-y*-1=-2x*-1+2*-1

Multiply -y by -1 to get y.5x+3y=7
y=-2x*-1+2*-1
Simplify the right-hand side of the equation by multiplying out all the terms.5x+3y=7
y=2x-2
Replace all occurrences of y with the solution found by solving the last equation for y.  In this case, the value substituted is 2x-2.5x+3(2x-2)=7
y=2x-2
Multiply 3 by each term inside the parentheses.5x+(6x-6)=7
y=2x-2
Since 5x and 6x are like terms, add 6x to 5x to get 11x.11x-6=7
y=2x-2
Since -6 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 6 to both sides.11x=6+7
y=2x-2
Add 7 to 6 to get 13.11x=13
y=2x-2
Divide each term in the equation by 11.(11x)/(11)=(13)/(11)
y=2x-2
Simplify the left-hand side of the equation by canceling the common terms.x=(13)/(11)
y=2x-2
Replace all occurrences of x with the solution found by solving the last equation for x.  In this case, the value substituted is (13)/(11).x=(13)/(11)
y=2((13)/(11))-2
Multiply 2 by each term inside the parentheses.x=(13)/(11)
y=(26)/(11)-2
To add fractions, the denominators must be equal.  The denominators can be made equal by finding the least common denominator (LCD).  In this case, the LCD is 11.  Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.x=(13)/(11)
y=-2*(11)/(11)+(26)/(11)
Complete the multiplication to produce a denominator of 11 in each expression.x=(13)/(11)
y=-(22)/(11)+(26)/(11)
Combine the numerators of all fractions that have common denominators.x=(13)/(11)
y=(-22+26)/(11)
Add 26 to -22 to get 4.x=(13)/(11)
y=(4)/(11)
This is the solution to the system of equations.x=(13)/(11)
y=(4)/(11)