what is the solution of the following system of equations?
1.) 5x + 7y =3
2x = -3y +1
To find the solution of the system of equations, we can use the method of substitution. Here are the steps:
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve equation 2 for x in terms of y.
2x = -3y + 1
Divide both sides by 2:
x = (-3y + 1)/2
Step 2: Substitute the value of x from step 1 into the other equation.
Replace x in equation 1 with (-3y + 1)/2:
5((-3y + 1)/2) + 7y = 3
Step 3: Simplify and solve for y.
Distribute 5:
(-15y + 5)/2 + 7y = 3
Multiply every term by 2 to remove the fraction:
-15y + 5 + 14y = 6
Combine like terms:
-y + 5 = 6
Subtract 5 from both sides:
-y = 1
Multiply both sides by -1 to isolate y:
y = -1
Step 4: Substitute the value of y into one of the original equations.
Substitute y = -1 into equation 2:
2x = -3(-1) + 1
2x = 3 + 1
2x = 4
Divide both sides by 2:
x = 2
Therefore, the solution to the system of equations is x = 2 and y = -1.
To find the solution to the given system of equations, we can use the method of substitution or elimination.
Let's use the method of substitution:
1.) 5x + 7y = 3
2.) 2x = -3y + 1
We can rewrite equation (2) to solve for x:
2x = -3y + 1
Dividing both sides by 2:
x = -(3y/2) + 1/2
Now, substitute the value of x in equation (1) using the expression we got for x:
5(-(3y/2) + 1/2) + 7y = 3
Simplifying equation (1):
-15y/2 + 5/2 + 7y = 3
Multiply through by 2 to eliminate fractions:
-15y + 5 + 14y = 6
Combine like terms:
-y + 5 = 6
Subtract 5 from both sides:
-y = 1
Multiply through by -1 to get y:
y = -1
Now, substitute the value of y into equation (2) to find x:
2x = -3(-1) + 1
Simplifying equation (2):
2x = 3 + 1
2x = 4
Divide both sides by 2 to solve for x:
x = 2
Therefore, the solution to the given system of equations is x = 2 and y = -1.
5x + 7y = 3
2x + 3y = 1
Multiply first equation by 2 and second by 5. Subtract first equation from second.