Solving a system of equations

If 2x + 3y = 4  and  5x + 6y = 7,  what is the value of 8x + 9y ?
A.)  -10
B.)  -1
C.)  2
D.)  7
​E.)  10

---

Find the values of x and y from the given system of equations, then substitute those values into 8x + 9y.

Solve the system.

2x + 3y = 4
5x + 6y = 7

-4x - 6y = -8   {multiplied first equation by -2}
5x + 6y = 7   {second equation stays the same}
----------------
x = -1   {added the two equations}

Substitute the value of x into one of the two equations to solve for y.

2x + 3y = 4   {first equation}
2(-1) + 3y = 4   {substituted -1, in for x, into first equation}
-2 + 3y = 4   {multiplied 2 by -1}
3y = 6   {added 2 to each side}
y = 2   {divided each side by 3}

Substitute -1 for x and 2 for y, into the expression 8x + 9y.
​
8x + 9y
=  8(-1) + 9(2)   {substituted -1 for x and 2 for y}
=  -8 + 18   {multiplied}
=  10   {added}

E.)  10

Ask Algebra House