to solve the system of equations which expression could be substituted for x into the first equation? first: 2x+7y=10 second: x-2y=15
x = 15+2y
2x+7y=10
Substitute 15+2y for x in second equation and solve for y. Insert that value into the first equation and solve for x. Check by inserting both values into the second equation.
To solve the system of equations using substitution, we need to isolate one variable to substitute into the other equation. Let's isolate x in the second equation, which is x - 2y = 15.
Adding 2y to both sides of the equation, we get x = 2y + 15.
Now, we can substitute this expression, 2y + 15, for x in the first equation, which is 2x + 7y = 10.
Replacing x with 2y + 15, the equation becomes 2(2y + 15) + 7y = 10.
Now we can simplify and solve for y.
To solve the system of equations, we need to find the values of x and y that satisfy both equations. To do this, we can use substitution.
First, we need to choose an expression that represents x. This expression should allow us to easily substitute it into the first equation to eliminate x and solve for y.
Looking at the second equation, we can solve it for x by adding 2y to both sides:
x = 15 + 2y
Now we have an expression for x that we can substitute into the first equation:
2(15 + 2y) + 7y = 10
Simplifying the equation:
30 + 4y + 7y = 10
30 + 11y = 10
Next, we isolate the variable y:
11y = 10 - 30
11y = -20
And solve for y:
y = -20/11
Once we find the value of y, we can substitute it back into the second equation to solve for x:
x - 2(-20/11) = 15
x + 40/11 = 15
To solve for x, we isolate the variable:
x = 15 - 40/11
Simplifying:
x = (165 - 40)/11
x = 125/11
Therefore, the solution to the system of equations is x = 125/11 and y = -20/11.