Solve by substitution: y = 2x + 3; y = −5x − 4
Since both equations are already solved for y, we can substitute the value of y from one equation into the other equation.
Substitute y = 2x + 3 into the second equation:
2x + 3 = -5x - 4
Now solve for x:
2x + 5x = -4 - 3
7x = -7
x = -7/7
x = -1
Now substitute this value of x into either of the original equations to solve for y.
For y = 2x + 3:
y = 2(-1) + 3
y = -2 + 3
y = 1
Therefore, the solution is x = -1 and y = 1.
To solve this system of equations using the substitution method, follow these steps:
Step 1: Start with the first equation and solve it for y.
y = 2x + 3
Step 2: Substitute the expression for y from Step 1 into the second equation.
-5x - 4 = 2x + 3
Step 3: Solve for x.
Combine like terms: -5x - 2x = 3 + 4
-7x = 7
Divide both sides by -7: x = -1
Step 4: Substitute the value of x from Step 3 into the first equation to find y.
y = 2(-1) + 3
y = -2 + 3
y = 1
So, the solution is x = -1 and y = 1.